Misplaced Pages

Revision as of 13:59, 15 July 2009

This page is not a forum for general discussion about centrifugal force. Any such comments may be removed or refactored. Please limit discussion to improvement of this article. You may wish to ask factual questions about centrifugal force at the Reference desk.

Physics Start‑class

This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Misplaced Pages. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.PhysicsWikipedia:WikiProject PhysicsTemplate:WikiProject Physicsphysics Start This article has been rated as Start-class on Misplaced Pages's content assessment scale. ??? This article has not yet received a rating on the project's importance scale.

This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (Learn how and when to remove this message)

Archives

April 2004 June 2004 – January 2006 January 2005 – November 2006 February 2007 – April 2007 January 2007 – March 2008 April 2008 May 2008 June 2008 July 2008 – August 2008 September 2008 October 2008 August 2008 – May 2009 May 2009 – ???

Unsourced assertions

Dick: I don't know where you get the idea this stuff you deleted is unsourced. Just prior to the footnote the numbers are provided with their sources. Then in the footnote itself a pdf file is cited from the geodesic society that gives the accepted number for 1/f. So the two estimates are sourced and irrefutable. Is the problem that calculating the 23% difference is unsourced arithmetic? Would you like a sub-section with sources explaining how to calculate a percent error??? Or could it be that you just did a knee-jerk reaction here without realizing the numbers all are sourced?Brews ohare (talk) 22:36, 25 June 2009 (UTC)

The footnote read "The error looks worse if the common measure of flattening f is used (see Clairaut's theorem), the ratio of the difference between semi-major and semi-minor axes divided by the semi-major axis. The flattening by Newton is f = 1/230, while that from the measurements is f = 1/298.4623304, an error of about 23%. See also Table 1.1 of the report by the International Association of Geodesy."

The assertion that "the error looks worse" is unsourced. The number 1/298.4623304 is unsourced, even though a statement of 10 significant digits practically screams for a source. The linked article has a different number, and fewer digits. The "error of about 23%" is your interpretation of the relationship between the numbers, I presume, but is there a source for that way of comparing flattening? No source provided. I don't understand how you don't understand what unsourced means. Read WP:V and WP:RS. Dicklyon (talk) 05:12, 26 June 2009 (UTC)

Well Dick here is how it goes. The modern estimates of semimajor and semiminor axes are sourced as the values 6356.77 km & 6378.14 km leading to an f of (6378.14 - 6356.77)/6378.14 = 0.003350 or 1/298.4623. The cited Table 1.1 has f = 1/298.25642±10, not enough different to matter here. Newton's numbers are sourced as a ratio of diameters of 229 to 230 or an f =(230-229)/230 = 1/230 = 0.004348. Taking the modern estimate as the more accurate the size of percent error is (|0.003350- 0.004348|)/0.004348 × 100 ≈ 23 %. How would you like this information to be presented? For a definition of flattening f see Clairaut's theorem. Brews ohare (talk) 05:38, 26 June 2009 (UTC)

Inertia

Dick, what you have done is to replace a more specific meaning (momentum) with a more general term (inertia) that has got at least two meanings. Even if you look at the wikipedia article about inertia, you will see that some editor has realized that the word inertia has got a common meaning of momentum which differs from its more accurate meaning of 'resistance to change'.

As regards 'centrifugal force', when we use the word inertia in this context, we are talking about momentum as opposed to the more accurate meaning of inertia which is 'resistance to change'.

I think that your reversion of my clarifying edit was motivated more by your own inertia (in the more accurate sense of the word) rather than by any desire to help clarify the wording.

Your point about the momentum being orthogonal to the centrifugal force is a true fact in its own right but it in no way diminishes the accuracy of stating that centrifugal force is an outward force that is associated with momentum.

It can of course be argued that the whole essence of momentum is its resistance to change, hence making the two meanings tend to blend into one. But there is still a subtle distinction between the two meanings because by the same token, we can equate inertial mass with inertia, yet nobody is trying to say that momentum is the same thing as inertial mass. The word inertia truly is a classical archaic broad spectrum terminology. I was merely trying to write the introduction using modern scientific terminologies.

On reflection, how about simply stating that centrifugal force is the outward force that arises in connection with rotation, and totally dropping all mention of either inertia or momentum? The simpler the introducing line, the better. David Tombe (talk) 11:34, 5 July 2009 (UTC)

Planetary Orbital Theory

FyzixFighter, you have removed a fully sourced section on the false grounds that Leibniz's views are already covered in the history section. That has got nothing to do with the fact that the planetary orbital equation in question is still used in modern textbooks. This is nota matter of history. I am therefore going to restore the section because it is accurate, fully sourced, and totally relevant to the topic. What legitimate reason can you possibly have for objecting to its inclusion? Even if you think that the centrifugal force in question is a manifestation of the fictitious force, that is still not a reason to remove the information in question. David Tombe (talk) 16:17, 9 July 2009 (UTC)

If it's going to be in there, it needs to point out that it's talk about a pseudo-force induced by the fact that the r coordinate is measured along a vector that is co-rotating with the planet, and that it's just a special case of that rotating system approach. Probably should be integrated into the relevant section. Dicklyon (talk) 17:47, 9 July 2009 (UTC)

I agree with you in part Dick. The planetary orbit equation is a subset/special case of the fictitious force concept. It really is only of interest in this general article in terms of the history of centrifugal force. Multiple sources have been provided that explicitly state that Leibniz's centrifugal force is tied a rotating frame. For example, from the Swetz reference about Leibniz's and Newton's early concept of centrifugal force:

"Considered as an endeavor of the circulating body, or a force acting on the body itself, does not exist. But if we consider a reference frame fixed in a the body and rotating with it, the body will appear to have an endeavor to recede from the centre. This of course is a fictitious force reflecting the acceleration for the reference frame."

Therefore, I'm going to fold some of the disputed section into the history section where most of the material in the disputed section appears. --FyzixFighter (talk) 19:43, 9 July 2009 (UTC)

I agree, but I wouldn't object if it also had a brief mention in the section on fictitious force in rotating frames. Dicklyon (talk) 19:56, 9 July 2009 (UTC)

The fact that planetary orbits can be dealt with without involving rotating frames of reference means that rotating frames are not an essential part of the analysis. It may well be that some textbooks have tried to integrate the Kepler problem into the rotating frame of reference analysis, but that is no reason for consigning the topic of planetary orbits to the history section.

You have both stated your own opinion that the centrifugal force in planetary orbits is a special case of the fictitious force in a rotating frame of reference. Since you have got sources which agree with your opinion, you are entitled to add that opinion to the section which I put in yesterday. However, I will also add on top of that my opinion that planetary orbital theory does not require a rotating frame of reference in the analysis, and I will also cite sources to back that idea up. At any rate, there was absolutely no justification whatsoever for deleting that new section on planetary orbits lock, stock, and barrel, without any discussion on the talk page. David Tombe (talk) 11:51, 10 July 2009 (UTC)

Hi David: As you know, the Lagrangian approach does not explicitly involve any reference frame: it just picks out the Jacobi coordinates and cranks away. So to that extent the rotating frame is not "an essential part of the analysis". However, the analysis can be done many ways, and while the Lagrangian method may have the advantage of being an approach with wide application, the other methods based upon explicit use of rotating frames arguably have more (or at least different) intuitive content. Evidently, intuition is a fallible guide, but it is a great source of innovation. Brews ohare (talk) 14:58, 10 July 2009 (UTC)

Brews, I have no major quarrel with the Lagrangian approach in this respect. However I do think that Lagrangian can be seriously lacking when it comes to gyroscopic analysis. Lagrangian is an 'energy accountancy' system, but it is totally silent as regards crucial causative forces such as the axial Coriolis force which prevents a spinning gyroscope from toppling under gravity.

As regards rotating frames, it does indeed seem that some attempts have been made to do the Kepler problem within the context of rotating frames. But I can't see how the angular velocity that is associated with a rotating frame can be in any way adequate to deal with all the permutations of pairs of mutual angular velocity as would occur in two adjacent two body Kepler orbits. This scenario is what Maxwell used to generate the very real centrifugal force of repulsion between his vortices to account for magnetic repulsion.

Furthermore, trying to strap a rotating frame of reference around a two body planetary orbit would be a most cumbersome endeavour as it would involve a variable angular velocity. Why bother? As far as I am concerned, we only need to introduce rotating frames of reference if the actual physical scenario being analyzed contains one naturally. For example, in meteorology, we have the Earth and the entrained atmosphere. That is ideal for the introduction of a rotating frame analysis. Radial water pipes on rotating turntables would be another such example. David Tombe (talk) 15:36, 10 July 2009 (UTC)

The main reason for my removal of the planetary orbit section is that it is a special case of either one of the two more general sections. And actually Brews has summed up one of the reasons why I didn't fold the planetary orbit stuff into the rotating frame fictitious force section. This is supposed to be a general article which should cover the material generally and direct to the more specific articles. That means we describe the two Newtonian mechanics uses of the phrase, the Lagrangian mechanics use of the phrase, and the history of the term and its importance in the whole absolute rotation debate. I don't see the centrifugal force of planetary motion as a separate and distinct topic from these general topics. The planetary motion figures prominently in the history section, so that's why I merged the info into there. But I don't see why it should get special mention outside of that section. Again, it's a special case of the general fictitious/inertial/pseudo- centrifugal force - associated with a non-stationary frame (or in other words, refers to terms moved from the acceleration to the force side of F=ma) in Newtonian mechanics or to extra terms that appear in the generalized force of Lagrangian mechanics.

So because this is the general centrifugal force article, I'm going to again remove the special case subsection - remerging the information into the history section. I'm also going to try my hand at expanding the intro and the fictitious force section to include the three contexts that Lagu brought up. --FyzixFighter (talk) 18:36, 10 July 2009 (UTC)

I think your argument about the role of this page is valid. The example appears in some form on the rotating CF page, but I'm not sure it is all covered there.

The "three contexts" introduces under the guise of polar coordinates what is really a Lagrangian attack on the problem, and discussion of this aspect should go there. See the following comments under #Three contexts. Brews ohare (talk) 21:57, 10 July 2009 (UTC)

Hey Brews, I hope you don't mind me merging the planetary orbit example into the main subsection. I think a separate sub-subsection of an example starts getting too far into a specialized article, but to come to a compromise we can all agree on I left in a good portion of it but moved it to were I felt it would flow well with the more general text right after the central potential discussion. I also trimmed some of the historical Leibniz stuff since (1) it's covered in the history section and (2) I think Leibniz didn't derive it using Lagrangian mechanics, but with a formalism that more closely paralleled Newton. In your opinion is this an equitable solution? If not, why and what would you suggest as a compromise? --FyzixFighter (talk) 22:32, 10 July 2009 (UTC)

There is only one universal centrifugal force. The planetary orbit is a very important manifestation of that force and hence it needs to have a section of its own. It is in fact the most general manifestation of the centrifugal force. The planetary orbit example can then be extended to the rotating spheres example by attaching a string between the two objects when they are in a state of mutually outward motion. The string will be pulled taut. This is the so called 'reactive centrifugal force' kicking in , which in turn induces an inward centripetal force due to the tension in the string.

It is wrong to claim that the centrifugal force in planetary orbits is a special case of the 'rotating frame' centrifugal force. We don't need a rotating frame in order to analyze the planetary orbital problem and the centrifugal force in the Leibniz equation is a 'polar coordinates' centrifugal force measured relative to the inertial frame. The centrifugal force in a planetary orbit is the centrifugal force that is built into the inertial path. That centrifugal force is just as much the so-called 'reactive centrifugal force' as it is any other kind of centrifugal force. Indeed, it was in the context of planetary orbits that Newton concocted the concept of the 'reactive centrifugal force'.

Hence, we put in a short and simple section on planetary orbits, much as Brews has just done, and we give that section the appropriate title. There is no need to juggle it all around and merge sections together in order to try and dilute the planetary orbit concept and the Leibniz equation. David Tombe (talk) 00:45, 11 July 2009 (UTC)

Brews's alternative section

Brews, your alternative section covers the main points. I will not make any amendments to it until I have studied the details. At the moment, I am wondering whether or not the variable r is the distance to the centre of mass as you say, or if it is the actual distance between the two objects. I have a feeling that it is the latter, but I need more time to think about it. David Tombe (talk) 12:09, 10 July 2009 (UTC)

On thinking more about it, it's probably OK because I can see that you have used the language of reduced mass. David Tombe (talk) 14:22, 10 July 2009 (UTC)

David: Are the initial energy and angular momentum sufficient to determine the solution? The angular momentum is subsumed under the parameter ${\displaystyle \ell }$, but the equation is second order and so appears to need another initial condition. Brews ohare (talk) 15:07, 10 July 2009 (UTC)

Brews, The general solution is a conic section. A conic contains two parameters that need to be determined. One is the eccentricity and the other is the semi-latus rectum. As you say, we are dealing with a second order differential equation, and hence we will have two arbitrary constants that need to be determined. I do believe from memory that the two arbitary constants in question are indeed the eccentricity and the semi-latus rectum. The eccentricity is determined by the initial kinetic energy for the particular radial distance at the kick-off point. The semi-latus rectum is determined by the angle of projection.

It's thirty years since I did these problems in applied maths and I'm rusty. If you have any more questions, I'll look it up for you. But I can now see that we are dealing with three factors that determine the full solution. Not only do we have the initial kinetic energy and angle of projection, but also the initial radial distance. However, I think that when all combined, this will reduce to initial energy and initial angular momentum. I remember a formula for the eccentricity which involved speed and radial distance. David Tombe (talk) 15:23, 10 July 2009 (UTC)

Three contexts

The third context is equivalent to the Lagrangian discussion and duplicates points made in that section. I have added the references.

This topic is separate from the "rotating reference frame" topic because it (i) doesn't invoke a rotating frame (ii) has applicability where no rotating frame is involved and (iii) leads to endless confusion when believed to have some connection to Newton's fictitious forces. For example, the "third context" centrifugal force is not "fictitious" because it doesn't vanish when the frame doesn't rotate. Brews ohare (talk) 21:47, 10 July 2009 (UTC)

Thanks Brews for the edit. I really prefer how you've connected the "third context" to the Lagrangian formalism than how I had included the idea. My only minor qualm is more about policy than content. The Bini article which introduces the "three contexts" does all three from a Newtonian mechanics viewpoint. In Bini's third context, F=ma is written out in polar coordinates and then, to make the equation look like the Cartesian coordinate counterparts (ie ${\displaystyle m{\ddot {\eta }}=\sum F_{\eta }}$), we move Goldstein 3-12's "centripetal acceleration term" over to the force side and call it a force. Personally I much prefer your redirection to the Lagrangian formalism since, IMO, arbitrarily moving a term from one side of the equation to the other does not suddenly transform it from a term in the radial acceleration to a force term. When this is done, it completely throws the Newtonian definition of "force" out the window. But the Lagrangian formalism gives moves all the arbitrariness to the choice of coordinates (where it should be) and in a consistent and logical fashion cranks out the "generalized forces". However, again I worry if casting the third context as an extension of the Lagrangian formalism strays to far from the (IMO somewhat lacking and disingenuous) description in the Bini source. --FyzixFighter (talk) 22:26, 10 July 2009 (UTC)

FyzixFighter, you are making alot of unnecessary complications. There is only one centrifugal force. I'm happy enough to have a section on the Lagrangian treatment of centrifugal force. But we do not mix such a section with the Leibiz treatment of the Kepler problem. The Leibniz equation is not a Lagrangian equation. It is a force equation. It is a second order differential equation in the radial distance. Lagrangian mechanics is about conservation of energy.

And as regards moving things from one side of an equation to the other, that never converts a centrifugal force into a centripetal force. You are getting the inertial path equation mixed up with the two body Kepler problem. The former does not involve a gravitational field and it is a hypothetical situation which never exactly happens in nature. The latter has a gravitational field involved. The term that refers to centrifugal force in the latter refers to centripetal force in the former. There is no moving terms to the other side of the equation going on. They are two different equations for two different physical secnarios. David Tombe (talk) 00:53, 11 July 2009 (UTC)

David, Leibniz's equation can't be a force equation, at least not in the standard, Newtonian mechanics definition of force. There are only two ways to get Leibniz's equation from first principles: using Lagrangian mechanics or Newtonian mechanics. When the two body Kepler problem is done using Newtonian mechanics, the only force that needs to be included in F_net is gravity - no centrifugal force is included in the sum of forces. As Bini and Strommel note, the ${\displaystyle -mr{\dot {\theta }}^{2}}$ term in the radial acceleration (which Goldstein calls the centripetal acceleration term) is moved to the force side of the equation - that is how the centrifugal force term arises. It's not a real force, it's just a term from the radial acceleration that we've moved. See the end of Strommel's discussion on pg. 36-38. Bini also classifies it this as a fictitious force that is implied by the frame of reference. --FyzixFighter (talk) 03:43, 11 July 2009 (UTC)

FyzixFighter, you are just playing around with words. The Leibniz equation and planetary orbits are the most general way of explaining centrifugal force. You don't want it in the article because it doesn't involve the use of a rotating frame of reference. It's as simple as that. All your arguments above are totally specious. David Tombe (talk) 09:00, 11 July 2009 (UTC)

At least three references explicitly support the "fictitious" interpretation of Leibniz's centrifugal force (two of which you initially provided):

• From Swetz, "Learn from the Masters!", pg 269

Considered as an endeavor of the circulating body, or a force acting on the body itself, does not exist. But if we consider a reference frame fixed in a the body and rotating with it, the body will appear to have an endeavor to recede from the centre. This of course is a fictitious force reflecting the acceleration for the reference frame.

• From Linton, "From Eudoxus to Einstein", pg 413

Newton had realized crucially that it was much simpler to consider things from a frame of reference in which the point of attraction was fixed rather than from the point of view of the body in motion. In this way, centrifugal forces - which were not forces at all in Newton's new dynamics - were replaced by forces that acted continually toward a fixed point.

• From Aiton, "The celestial mechanics of Leibniz in the light of Newtonian criticism"

Leibniz viewed the motion of the planet from the standpoint of a frame of reference moving with the planet. planet. The planet experienced a centrifugal force in the same way that one experiences a centrifugal force when turning a corner in a vehicle. From the standpoint of an observer outside the vehicle the centrifugal force appears as an illusion arising from the failure of the traveller to take account of his acceleration towards the centre. Although both standpoints are valid, Newton, in the Principia, always used a fixed frame of reference.

and

Leibniz's study of the motion along the radius vector was essentially a study of motion relative to a rotating frame of reference.

So if we get to Leibniz's equation from Newtonian mechanics (ie the traditional definition of force), his centrifugal force is a fictitious force that vanishes from the list of forces acting on an object in Newton's 2nd law when the dynamics is described from the inertial frame. --FyzixFighter (talk) 13:47, 11 July 2009 (UTC)

FyzixFighter, centrifugal force only appears to vanish in the inertial frame of reference when the inertial path is described in Cartesian coordinates. It shows up when we use polar coordinates. And yes, the centrifugal force in planetary orbits is the same centrifugal force that arises in the Lagrangian formulation, and in the rotaing frames formulation in the special case of co-rotation. But that is not a basis for hiding a section on planetary orbits inside the Lagrangian section as you have been attempting to do. This article is about 'centrifugal force'. The sections of the article are for the purpose of illustrating centrifugal force. Planetary orbits present the best directly observed illustration of centrifugal force as an outward inverse cube law force. The equation which was used in that section by both myself and Brews was Leibniz's equation. Leibniz's equation is not Lagrangian mechanics even if it is being used to describe something that can equally be described using Lagrangian mechanics. So you have got absolutely no grounds whatsoever to hide this section inside the Lagrangian section.

Likewise with the centrifugal force in the inertial path. Polar coordinates do not involve a rotating frame of reference. The 'inertial path' centrifugal force is indeed the same centrifugal force that arises when an object co-rotates with a rotating frame of reference. But that is not grounds for deleting all mention of the treatment of centrifugal force in connection with polar coordinates in the absence of rotating frames.

As for your extension to the introduction, you cannot be serious. It doesn't exactly read very well. What is the point of your extension? David Tombe (talk) 19:02, 11 July 2009 (UTC)

Look again at both the Bini and Stommel reference which talk about the polar coordinate centrifugal force. Both call it a fictitious force. For example from Bini after discussing the different CF contexts including the polar coordinate context:

"In other words, the "fictitious" centrifugal force is a convenience that only has meaning with respect to some implied reference frame"

And from Stommel:

"Sometimes equation (2.14a) is written with one of the acceleration terms on the righthand side

${\displaystyle {\ddot {r}}=r{\dot {\theta }}^{2}+F_{r}}$.

The term ${\displaystyle r{\dot {\theta }}^{2}}$ then looks like a force, and it actually has a name: "the centrifugal force" . It is always positive and directed away from the origin. But it is really not a force at all, and so if we want to make use of it in a formal sense, then we could call it a virtual, fake, adventitious force."

This is because, as Stommel states, ${\displaystyle {\ddot {r}}}$ is not the true radial acceleration, the true radial acceleration is ${\displaystyle {\ddot {r}}-r{\dot {\theta }}^{2}}$. While Leibniz's radial equation is mathematically valid, since ${\displaystyle {\ddot {r}}}$ is not the radial acceleration, then we cannot use Newton's 2nd law to interpret the other side as a true force or sum of forces. It's that simple. In polar coordinates in the inertial frame, the ${\displaystyle mr{\dot {\theta }}^{2}}$ term is part of the acceleration, not a force acting on the circulating body. In all the fictitious CF cases, both the rotating frame contexts and the polar coordinates, the "centrifugal force" and other fictitious forces arise when we take Newton's 2nd law and start moving terms that appear in the acceleration, ${\displaystyle {\ddot {\vec {r}}}}$ and move them to the force side of the equation and interpret them as "forces". In the rotating frame case, the terms arise from the time dependency of the basis vectors for the rotating frame; in the polar coordinates, it's the centripetal acceleration term as Goldstein calls it. --FyzixFighter (talk) 21:24, 11 July 2009 (UTC)

RfC: Content dispute on Leibniz equation and inclusion of planetary orbit equation

Please consider joining the feedback request service. An editor has requested comments from other editors for this discussion. Within 24 hours, this page will be added to the following list: Maths, science, and technology When discussion has ended, remove this tag and it will be removed from the list. If this page is on additional lists, they will be noted below.

Ongoing content dispute over the different treatments of the centrifugal force and whether Leibniz's centrifugal force represents a distinct and separate concept. FyzixFighter (talk) 03:49, 11 July 2009 (UTC)

FyzixFighter, the centrifugal force in the Leibniz equation does not represent a distinct and separate concept as compared to any other approach to centrifugal force. There is only one centrifugal force. You are misrepresenting what this dispute is about. The dispute is about the fact that you have consistently attempted to remove all mention of the centrifugal force in connection with situations that don't require a rotating frame of reference in the analysis.

This latest round began when you removed my new section on planetary orbital theory. At first you tried to argue that it belonged in the history section. Brews then restored his own amended version of what I had written. You removed that too. After your attempts to remove it failed, you then blended it with the Lagrangian section when in fact the Leibniz equation has got nothing whatsoever to do with Lagrangian mechanics. David Tombe (talk) 08:57, 11 July 2009 (UTC)

My comment: There are exactly two sourced concepts of centrifugal force. The planetary one fits with the fictitious or pseudo force definition; it's due to measuring location r along a co-rotating direction vector. But David knows that already, just hasn't accepted it over the last year or so. Dicklyon (talk) 03:13, 12 July 2009 (UTC)

There are three sourced concepts, all in the article. One is the reactive CF, sometimes referred to as simply the CF. A second is the Newtonian CF, which appears only in rotating frames of reference and transforms as a vector force. A third is the Lagrangian generalized CF, which again is often referred to as CF, and has very little to do with the Newtonian concept, and a lot to do with a formal analysis based upon a space of generalized coordinates. The Lagrangian generalized CF has these differences from the Newtonian: (i) it does not require a rotating frame, (ii) it can be nonzero in an inertial frame (iii) it does not transform like a vector under coordinate transformations.

In the case of planetary motion involving only two bodies, the Newtonian analysis in a co-rotating frame is mathematically identical with the Lagrangian formulation based upon the Jacobi two-body coordinates (r, θ) as generalized coordinates. The Leibniz approach might be seen as a precursor of the Lagrangian method, as Leibniz' ideas about action had a lot to do with the background of the Lagrangian methodology.

Many physics problems can be approached with different intuitive ideas that lead ultimately to the same equations. That means they all predict the same thing. However, the intuitive notions behind the various schemes often are different, and may be valuable in themselves as they may point to useful ways to analyze other problems. The Newton scheme is tied to the notions of inertial frames and vector forces. The Lagrangian scheme is tied to variational principles based upon scalars. These intuitive schemes are not all the same, even if they all lead to the same mathematical equations. All roads lead to Rome, but all roads aren't the same road. So far, little stress has been placed upon whether the Leibniz scheme brings yet a fourth viewpoint to the problem. I don't know if it does or doesn't. Brews ohare (talk) 04:29, 12 July 2009 (UTC)

Ah, right, I forgot the Langrangian generalization. My "two" only applied to the conventional centrifugal forces. Dicklyon (talk) 04:35, 12 July 2009 (UTC)

I'd add that the inclusion of the Leibniz scheme is warranted in this particular article only if it brings a special viewpoint to the notion of centrifugal force. For example, does the Leibniz approach include ideas that lead more directly to the equations than the Lagrangian or the Newtonian views? If Leibniz' approach is of interest only as an example of one of the others, it is best dealt with in the the more detailed articles, rather than in this summary or pre-amble article. Leibniz' special viewpoint (if it exists) need not be dwelt upon here in great detail, but should be outlined in the appropriate more detailed article. Brews ohare (talk) 04:44, 12 July 2009 (UTC)

From my point of view, the Leibniz scheme is only interesting from the historical perspective. Three of the historical references we're using (Swetz, Linton, Aiton - I've listed the quotes in the above section) equate Leibniz's scheme to the special case in Newtonian mechanics of a co-rotating frame, ie that he was describing motion within a frame tied to the planet. I know we have sources, like Goldstein, that derive the radial equation using the Lagrangian scheme, but don't make a connection with Leibniz's ideas. What we need is a source that gives the details of Leibniz's reasoning. However, as far as I can tell when people use his radial equation today, they arrive at it via Newton and therefore an implied non-inertial frame, or via Lagrange in which case it's a generalized force. I don't think I've seen a consistent derivation of Leibniz's radial equation that is distinct from these two. --FyzixFighter (talk) 05:03, 12 July 2009 (UTC)

After perusing the Aiton reference, Aiton seems to support the rotating frame view of Leibniz's scheme. He states:

"Influenced perhaps by Galileo's treatment of the motion of projectiles, Leibniz was aware of the principle of vectorial composition of motion, as is evident from one of his letters to Huygens. Resolving the motion of the planet into components along and perpendicular to the radius vector respectively, he considered these component motions separately. The motion perpendicular to the radius vector gave rise to an outward force, acting on the planet, and it was this force that Leibniz termed the centrifugal force of the circulation. Leibniz attempted to relate the other component of the orbital motion, namely, that along the radius vector, to the forces acting in this line. Leibniz's study of the motion along the radius vector was essentially a study of motion relative to a rotating frame of reference. Eventually he succeeded in showing that the acceleration along the radius vector was proportional to the difference of the centrifugal force and the attraction."

and later

"Leibniz's centrifugal force arises from the acceleration of his frame of reference. The motion along the radius vector is a motion relative to a rotating axis and Leibniz understood that, relative to this axis, the body experienced a centrifugal force."

and in the end

"The use of a rotating axis was a distinctive feature of Leibniz's contribution."

Do we have any reliable sources that say otherwise, or that cast Leibniz's derivation within the framework of Lagrange or something similar to Lagrange? --FyzixFighter (talk) 06:06, 12 July 2009 (UTC)

FyzixFighter, you are completely missing the point. The point is that planetary orbits present an illustrative example of centrifugal force, and it is perfectly in order that such an example should be included in an article on centrifugal force. There are plenty of sources with quite a variety of methods which show that planetary orbital theory does not require a rotating frame of reference in the analysis. The fact that you can also produce sources that show that certain people have attempted the analysis using rotating frames of reference is not a justifiable reason for deleting the planetary orbital example or for relegating it to the history section. Planetary orbital theory is not history. David Tombe (talk) 12:10, 12 July 2009 (UTC)

David: You have not addressed the pertinence of an example in this article whose role is as a preamble to the other articles. As a preamble, its role is not to provide detailed examples, but to guide the reader to the appropriate other section. As such, the most that can be done here (assuming the Leibniz approach is subsumed) is to point out that centrifugal force in planetary motion is discussed at length in Centrifugal force (rotating reference frame) and in Mechanics of planar particle motion. Brews ohare (talk) 14:15, 12 July 2009 (UTC)

Brews, The problem is, which of the two re-direct articles would you send it to? I don't want to put it into the centrifugal force (rotating frames of reference) article when the topic in question is seldom dealt with in the context of rotating frames of reference. I had conceded that centrifugal force as a topic is dealt with on the modern science library shelves predominantly in connection with rotating frames of reference. I had conceded that point. But you should all likewise concede that planetary orbital theory is predominantly dealt with by methods that don't use rotating frames of reference, even if there are some exceptions. So I don't think that centrifugal force (rotating frames of reference) is the correct page for planetary orbits. As for the so-called reactive centrifugal force, there are some grounds for putting it there too. Some of you guys have been a little confused about the reactive concept and you have been wrongly trying to justify it in line with Newton's third law of motion. Unfortunately, it is not as simple as that. A web-link which Dick kindly provided, explains the history very well. Newton's reactive concept was born out of Leibniz's planetary orbital equation on specious grounds. I gave a clear quote from the 1961 Nelkon & Parker as to exactly what Newton's erroneous concept was. It was deleted and the correct definition of the reactive concept is not currently reflected in either this article or the 'reactive centrifugal force' article.

As you know, my own view is that the two re-direct articles should be deleted and this article should be the one single article on centrifugal force. Newton's erroneos reactive concept could be explained as a follow on to a section on planetary orbits and the Leibniz equation. Newton's erroneous concept still gives correct results for the special case of circular motion, and as you know, it is used by engineers. Alot could be written about the modern changing attitudes to centrifugal force citing examples of revised texts as in Nelkon & Parker (1961 v. 1970) and the Goldstein (1980 v. 2002). But unfortunately, even the revisionism has proved to be uncomfortable for certain editors.

We have material for a good interesting combined technical and historical article, but it is not getting off the ground because I have been working against too much opposition. There is opposition to anything that involves centrifugal force being exposed as an actual outward 'push' or 'pull' in the absence of rotating reference frames. And there is opposition to any mention of revisionism. That opposition needs to be examined. Why are certain editors so strenuously opposed to these things? It was actually you that wrote the current planetary orbital summary that has just been deleted. It is a re-write of my own version, but your version brings in 'reduced mass'. It is a very good short summary section. You really don't want to waste it. It gives interesting details such as the inverse cube law relationship for centrifugal force and the conic section shape of planetary orbits. It opens up the readers minds to the fact that centrifugal force has a variable value and is not simply an equal and opposite reaction to centripetal force as many people wrongly believe. David Tombe (talk) 17:29, 12 July 2009 (UTC)

Who is the intended audience for this page? I would suggest that it would be mainly students of physics. No one here has the expertise to write for a more advanced audience.

On that basis I would suggest that only one definition of centrifugal force (fictitious force) should be discussed in the main section of the article and that all other definitions should be moved to the history section. Martin Hogbin (talk) 21:37, 12 July 2009 (UTC)

The original purpose of this article was to have a short article summmarizing the different conceptions, and main links to the articles on the details at Centrifugal force (rotating reference frame) and Reactive centrifugal force. Unfortunately, it has become quite bloated. But it would be better to prune it back than to have it take over the role of Centrifugal force (rotating reference frame). Dicklyon (talk) 21:44, 12 July 2009 (UTC)

Yes, I see. In that case I think the title is a little misleading. It should something like 'Centrifugal force (different concepts) or 'History of centrifugal force'. Either that or the article should be pruned heavily and also make clear the concept that is most commonly taught today. Martin Hogbin (talk) 22:00, 12 July 2009 (UTC)

I would not agree that only one definition should be discussed, and do not agree that all others are somehow only of historical interest. The sources show all three versions have strong modern adherents. Brews ohare (talk) 21:48, 12 July 2009 (UTC)

Other concepts are of historical interest only are for anyone trying to understand the subject for the first time. Other uses of the term, which I am sure do still exist, are very confusing to beginners. It would be best to refer to them along the lines of, 'In some areas of engineering the term is used to mean...'. Martin Hogbin (talk) 22:00, 12 July 2009 (UTC)

It's not really different areas, just different conceptions. The reactive force concept is simple and easy to understand; the pseudo-force is more useful and more widely taught. We don't need this article at all except to summarize these two and dispatch to the main articles, in my opinion, but Brews jumped in the with the big middle section on "Centrifugal force and absolute rotation", which dispatches to more related articles, and the "Lagrangian formulation of centrifugal force", which I'm still not sure what to make of. Perhaps he's trying to attract some readers to his articles Bucket argument, Rotating spheres, Clairaut's theorem, Mechanics of planar particle motion, etc. Maybe he's actually writing a book, and these are his chapter drafts. Hard to say... Dicklyon (talk) 22:12, 12 July 2009 (UTC)

I disagree that the reactive concept is easy to understand. It might be easy to apply in some cases where the physics is not important but what is described as 'revisionism' in this article is the realization by teachers of physics that the reactive concept of CF is confusing to most students.

If we use this page as a short disambiguation type page then we should still make clear that the only concept taught to students of physics is the 'rotating frames' one. Martin Hogbin (talk) 22:28, 12 July 2009 (UTC)

Most common, yes; but only, no. Here's a 2004 physics book that teaches the reactive CF. Here is a 2001 book that has it both ways. There are lots of other examples, so let's not push a single POV when there are several that can be represented as easily as one. Dicklyon (talk) 22:37, 12 July 2009 (UTC)

Your first reference clearly describes the reaction force as the centrifugal reaction. It then goes on to describe the centrifugal force in terms of a rotating frame. For this article to call what the book describes as a centrifugal reaction as the centrifugal force is confusing and incorrect.

The second source clearly describes CF as an apparent force in a rotating system. Martin Hogbin (talk) 08:18, 13 July 2009 (UTC)

Yes, you're right; the first uses the term "centrifugal reaction" for what we're calling reactive centrifugal force; the second says "the reaction to this force is the centrifugal force. Here is a 2002 Physics for Geologists book that teaches "the centripetal force (the equal and opposite reaction being the centrifugal force)". These are not "incorrect", just a different thing than the one thing that you want to call correct; it's OK to discuss what we think is correct, but in the article we need to represent actual uses, and try to de-confuse them rather than pretending there's only one. The point of this article was to compare and contrast these two things, and vector off to the main articles on each; but it has gotten way out of control, as you can see. The comparison table was one that Brews made up to try to explain the difference to David, and I recommended we use it here for this purpose; I think it makes very clear that the two things called centrifugal force are two different thingss. In the process, I also learned that there are two things called centripetal force, but they're usually nearly the same; sometimes in a planetary orbit situation, the central force is taken to be centripetal, even for non-circular orbits, but the more strict definition usually taught is that the centripetal force is only the component perpendicular to the velocity vector. It's another case where it would be better to show both uses and compare them, rather than pretend the "incorrect" one doesn't exist. Dicklyon (talk) 22:27, 13 July 2009 (UTC)

The Roche reference used in the article is the one that I have found the most helpful with respect to your question Martin. In it he states:

What question?

"I have identified at least three interpretations of centrifugal force in the literature: a valid meaning in physics, an entirely different but equally valid meaning in engineering, and a cluster of false meanings."

He later clarifies the engineering definition:

"But we must leave the final word to the engineers. The stresses that develop in rapidly rotating turbine blades are thought of by mechanical engineers as being due to centrifugal forces. To take a simple example, an object whirled on an elastic string pulls the string outwards, creating the tension in the string. Both the inertial centrifugal force acting on the string and the elastic centripetal force acting on the moving body are reaction forces—they call each other into existence. Centrifugal and centripetal force are equal and opposite here but do not balance because they act on different bodies.

In a rotating turbine, for example, each outer section of the blade exerts an outwards pull on the portion between it and the shaft, while at the same time the latter exerts an elastic inwards pull on the former. It is the stresses in the blades and their causes that mainly interest engineers, rather than the centripetal forces. It follows that both elastic centripetal forces and inertial centrifugal forces act in a rotating solid body."

The Kobayashi reference says something similar:

"The term centrifugal force then has two meanings: one is the inertial force due to the rotation of the noninertial frame relative to the inertial frame and the other is the reaction force of the centripetal force to produce acceleration toward the center of rotation. The origins of these forces are different from each other."

--FyzixFighter (talk) 15:10, 13 July 2009 (UTC)

Yes, I know. What is the point of this article? Who is it intended to help and what is it intended to help them do? Martin Hogbin (talk) 16:14, 13 July 2009 (UTC)

Sorry, I misunderstood your concern. I meant to address your comment that the rotating frame/fictitious CF is the only concept taught today. Is not just physics education that we need to address, but also engineering education in which the reactive centrifugal force and Lagrangian centrifugal force are not just a historical conceit. Anyways, sorry again for the misunderstanding and thanks for starting the section below. --FyzixFighter (talk) 19:16, 13 July 2009 (UTC)

• Oppose introduction of Leibniz inverse cube centrifugal force. Now that I have understood what the question is I will state my opinion on the subject. Leibniz' treatment of CF as an outward-acting inverse cube force should only be presented in the history section. There should be no statement of an inverse cube law of centrifugal force in the rest of the article. Martin Hogbin (talk) 08:54, 14 July 2009 (UTC)

Martin, it's both history and present. The Leibniz equation is still the planetary orbital equation which is used in modern textbooks to obtain the elliptical, parabolic, or hyperbolic solutions for the two body problem. I have suggested an introduction section which deals with the conflict between Newton and Leibniz on this point, because it is very relevant to the three different aproaches which exist today for centrifugal force. David Tombe (talk) 13:15, 14 July 2009 (UTC)

The comparative table

One way or the other, something needed to be done about the comparative table because it didn't cater for situations in which centrifugal force is treated outside of the context of rotating frames of reference. An alternative approach would be to reduce it once again to two columns but amend the bit where it says 'rotating frame' in relation to the fictitious force, to read 'inertial frame'. In Lagrangian, polar coordinates, and co-rotation, the centrifugal force is measured relative to the inertial frame. It is only in non-co-rotation that any motion can be considered to be relative to the rotating frame of reference. David Tombe (talk) 19:23, 11 July 2009 (UTC)

I don't think such situations exist. The r in the planetary equation is clearly a measurement along a direction that co-rotates with the planet, such that treating its second derivative as an acceleration is exactly what that viewpoint is about. Dicklyon (talk) 03:10, 12 July 2009 (UTC)

David: You are right that the table is intended to clarify the difference between the reactive and the fictitious CF concepts. I don't think this table should be changed to include the Lagrangian CF, because it will make the whole comparison too complicated. Perhaps a second table should be constructed to contrast the fictitious CF and the Lagrangian CF? Brews ohare (talk) 04:54, 12 July 2009 (UTC)

Brews, something certainly needs to be done to generalize the situation. I'm personally of the opinion that the Lagrangian centrifugal force, the polar coordinates centrifugal force, the rotating frames centrifugal force in the special case of co-rotation, and the Leibniz centrifugal force are all the same force. The so called reactive centrifugal force is merely a knock-on effect of that force. The problem with the original table was that it stated that the fictitious force arises in a rotating frame of reference. But we all know that the Lagrangian centrifugal force and the polar coordinates centrifugal force are relative to the inertial frame and definitely don't involve rotating frames of reference. Hence there is a dilemma which needs to be addressed one way or the other. By all means edit the table again, but you need to bear these points in mind when doing so. David Tombe (talk) 12:16, 12 July 2009 (UTC)

David, I think you go wrong in saying "we all know that the Lagrangian centrifugal force and the polar coordinates centrifugal force are relative to the inertial frame and definitely don't involve rotating frames of reference." Certainly we don't agree here. The polar coordinates centrifugal force is just a way to use a co-rotating reference frame; the Lagrangian approach is a generalization of that concept, which in the special case of planetary orbit with co-rotating r dimension is not different from it. None of these correspond to any forces in the inertial frame, as there are no such forces. Dicklyon (talk) 17:25, 12 July 2009 (UTC)

Dick, you've got it the wrong way around. Yes indeed the polar coordinates centrifugal force and the co-rotating frame centrifugal force are one and the same thing. But the polar coordinates are variables which are referenced to the inertial frame. One of those variables is angular displacement which is clearly relative to the inertial frame, and it is that angular displacement which appears in the centrifugal force formula. The centrifugal force is in the radial direction and that direction rotates, but that doesn't mean that the acceleration itself is relative to any rotating frame of reference. This seems to be the common mistake. People see that the radial vector rotates and they immediately jump to the erroneous conclusion that a rotating frame of reference must be involved. David Tombe (talk) 18:11, 12 July 2009 (UTC)

Forces don't depend on what coordinate system you measure things in. The forces and accelerations you get by analyzing things in polar coordinates in an inertial frame are the same as what you get by measuring in Cartesian coordinates; they just have different expressions. CF only comes in when you jump to interpreting the second derivative of r as acceleration, which makes sense only in a frame co-rotating with the vector along which you measure r. But I've explained that more than a dozen times over the last many months, so why am I wasting my keystrokes on you? Dicklyon (talk) 18:35, 12 July 2009 (UTC)

Dick, we'll have to agree to differ on that. But it's got nothing to do with the current dispute. The current dispute is over FyzixFighter's attempts to prevent the theory of planetary orbits from being used as an illustrative example of centrifugal force and as a means of stating that centrifugal force obeys the inverse cube law. You saw the short section that Brews wrote and which was essentially a revised version of what I wrote. It was a very helpful and informative section and very relevant to the topic. But you have chosen to side with FyzixFighter's decision to delete it. FyzixFighter's reasons are empty of any logic. He says that planetary orbits are a special case. They are not. They are the most general case of centrifugal force that exists. There is no other example of centrifugal force that you could show me that is not the inverse cube law centrifugal force in the planetary orbital equation. The rotating bucket or whatever, it's all the one and only inverse cube law centrifugal force as in the Kepler problem.

Nowhere now is it stated in the article that centrifugal force obeys an inverse cube law when angular momentum is conserved.David Tombe (talk) 19:30, 12 July 2009 (UTC)

If that's the dispute, let's fix it by putting this material into the section on the rotating frame approach. OK? Dicklyon (talk) 19:40, 12 July 2009 (UTC)

Dick, that is indeed the dispute. But I've already explained to Brews above why the 'rotating frames' re-direct is not an appropriate venue for this material. Whereby I have conceded that most modern textbooks treat centrifugal force in terms of the rotating frames approach, I think that you ought to equally concede that most textbooks don't use the rotating frames approach for planetary orbits. It is not accurate to insert the planetary orbital example under the banner of 'rotating frames of reference' when only a few sources treat the problem that way. The rotating frames re-direct is not an appropriate venue for that material.

Ideally we shouldn't have any re-directs. Centrifugal force related material should all be on this page. There is no need to have a separate article for 'reactive centrifugal force' and 'centrifugal force in rotating frames'. A common thread runs through all centrifugal force along with a historical narrative. The only appropriate alternative venues that I can think of are Kepler's laws of planetary motion, the Kepler Problem, and Orbits. I've already put it into Orbits. If you want a compromise, you might consider supporting the inclusion of Leibniz related stuff on centrifugal force in these articles along with a comment in this article referring the topic of centrifugal force in planetary orbits to these topics. — Preceding unsigned comment added by David Tombe (talk • contribs)

So that's the impasse we've been at for about 15 months. You add the planetary stuff as if it's something different, everyone objects and takes it out, and Brews reacts by adding more and more complexity. But no matter how you cut it, the material is way too much for a single article; this is supposed to be the summary article, not a place to collect all those other details and digressions. Maybe if we recognize the pattern we can adjust. Dicklyon (talk) 21:48, 12 July 2009 (UTC)

In this instance, what complexity did I add? Definition of notation, maybe? A one-line connection to Lagrangian formulation? "More and more", eh? No opportunity missed for gratuitous insult. Brews ohare (talk) 21:55, 12 July 2009 (UTC)

I'm just explaining how the article got to be so big, well away from its original intent. You only added a little over 1 KB on Friday, only about 10 KB in each of May and June, so maybe you're right – only half of it is from you. Dicklyon (talk) 22:28, 12 July 2009 (UTC)

No Dick, I didn't add the planetary stuff as if it was something different. I added it as an illustration of centrifugal force in a context which didn't need a rotating frame of reference in its analysis. So what particular point of view are you referring to that I haven't been able to persuade everybody else of? It's more a case of other editors reverting out of spite rather than anything to do with wikipedia's rules. And as regards Brews, I'll say in his defence that he appears to be the only one that is genuinely trying to learn, and acting on what he has learned. You and FyzixFighter have learned alot too, but you are not always willing to act on what you have learned. You both appear to have some investment in playing down the real push and pull aspects of centrifugal force, and so you are both keen to dress it all up in coordinate frame transformations.David Tombe (talk) 23:44, 12 July 2009 (UTC)

FyzixFighter is trying to provoke an edit war

FyzixFighter, you wrote this when you did you reversion,

"I still think planet orbits are a special case and should not be mentioned - - -".

Planetary orbits are indeed one specific illustrative case of centrifugal force. That is not a reason for arguing that they should not be mentioned in the article.

You began this edit war over a year ago on the grounds that my attempts to insert the planetary orbital approach were original research. Now that we all know that you were wrong in that regard, you are scraping the barrel. You are now down to the pathetic argument that planetary orbits shouldn't be mentioned because they are a special case.

Every example of centrifugal force is a special case. David Tombe (talk) 21:10, 11 July 2009 (UTC)

You do realize with that last revert you just surpassed the three reverts in a 24-hour period:

• 1st revert 23:24, 10 July 2009
• 2nd revert 09:03, 11 July 2009
• 3rd revert 18:39, 11 July 2009
• 4th revert 21:02, 11 July 2009

--FyzixFighter (talk) 21:32, 11 July 2009 (UTC)

It's strange how I can be the one to put in a new edit to improve the article. You come along in your usual fashion and delete it. Brews writes an alternative version of it. You delete it too. Brews an I both endeavour to retain his version in the article, and suddenly I am being accused of being in breach of the three revert rule.

What you really need to do is explain to everybody your real reason for intervening in this topic. You certainly aren't interested in it in the normal course of events. Your interest seems to be limited to reverting edits which I make. Your reasons for trying to keep the planetary orbital equation out of the article have changed dramatically over the last 15 months from allegations of original research to a mere statement of the fact that the centrifugal force in planetary orbits is a special case. I would hope that any administrators that are watching this will take note of that reason and ask themselves why you are trying so hard to keep that topic off the page on the mere grounds that you see it as a special case. Few others would ever be as concerned about that as you seem to be. And I hope that all the editors who agreed with you last year that I was trying to introduce original research can now see that the planetary orbital equation is not original research at all. We are now long past the stage of sources. The sources are well established and the authenticity is no longer in dispute. You really will need to come up with a better reason for trying to keep that section out of the article. David Tombe (talk) 22:00, 11 July 2009 (UTC)

He may be edit warring, but I think you get the credit for the provoking. If you'd respond sensibly to feedback, you could incorporate this special case in an acceptable way. But you never have responded sensibly to feedback, so on it goes. Dicklyon (talk) 03:08, 12 July 2009 (UTC)

Dick, let's analyze what you said more carefully. Are you saying that my insertion of planetary orbits as an illustrative example was the provocation? We all know that it is fully sourced and authentic and that it presents a clear picture of centrifugal force in action. Last April 2008 I tried to get this stuff in and FyzixFighter went to the administrator's notice board and complained. The administrators believed FyzixFighter that I was engaging in disruptive editing and trying to promote original research. I ended up finding myself arguing against up to eleven or twelve editors at once, and I got blocked repeatedly on dubious grounds. I ended up getting blocked permanently for the crime of communicating with another editor while blocked.

We all know now that what I was trying to insert was not original research. I am the one that has now requested administrator intervention. But unlike last year, the administrators don't want to get involved. They were very keen to get involved when they throught that planetary orbits were my original research, but now that that has proved not to be the case, they have all gone away.

FyzixFighter is still trying to veto the inclusion of the planetary orbital example, ultimately for reasons which aren't yet altogether clear. His original reason that it was my original research has collapsed and he is now scraping the barrel. He is arguing that planetary orbits are only a special case of centrifugal force and so shouldn't be included in the centrifugal force article. That argument would be laughed out of court because it is a nonsense argument. And having then realized that there were two editors trying to insert the relevant passage, he attempted to jettison it into the middle of the Lagrangian section where it didn't belong. The section contained no Lagrangian in it. He might as well have jettisoned it into the middle of the wikipedia article on giraffes. It's true that planetary orbits can be analyzed using the Lagrangian method, but that doesn't mean that planetary orbits as a topic in their own right should be categorized under 'Lagrangian mechanics'.David Tombe (talk) 12:33, 12 July 2009 (UTC)

David you're misrepresenting me on at least three counts:

1. In April 2008 I reported you for wikistalking editors who disagreed with you (ie undoing their constructive and anti-vandalism edits on completely unrelated articles). I find it interesting that you have never acknowledged wrong-doing in this matter.
2. I think have been very clear on why I am vetoing the inclusion of the planetary orbital example here - it's a special case. This is a general (preamble as Brews calls it) article. The planetary orbital example and centrifugal force discussion is already on the more specific pages. I'm not fighting for the removal of the planetary orbital example from those pages.
3. I wasn't the one who first put the planetary orbital example in the Lagrangian section. Brews was .

Since the RFC hasn't appeared to have brought in previously uninvolved editors, perhaps we should try WP:3O (I don't know if this would be appropriate since Dick and Brews are also involved, though currently not as vehemently as you and I), informal mediation, or formal mediation. Thoughts on the appropriate next step in WP:DR? --FyzixFighter (talk) 15:42, 12 July 2009 (UTC)

FyzixFighter, Planetary orbital theory is an illustrative example of centrifugal force. You, for whatever reason, have decided that you don't want this example to appear in the centrifugal force article. The reason which gave last year was that it was original research on my part, and you succeeded in convincing many editors that this was the case. Now that the truth has come out, most of those editors have gone home. You have nevertheless decided to continue to veto the inclusion of this topic on new specious grounds. Your new grounds are simply not a legitimate basis to keep this example off the page, and your insistence on keeping this topic hidden from view is having a detrimental knock-on effect in that you are putting unnecessary complications into the article in order to justify yourself. These extras are merely clouding the whole topic. Your latest extras in the introduction are incoherent and of no use to anybody. You have even changed your position from last month, from 'two kinds' to 'three kinds'. You are only confusing the whole article and you are changing with the wind according to who you can find to be on your side.

Planetary orbits expose the outward force that is generated due to transverse motion. The example can then be elaborated on to explain the so-called reactive centrifugal force simply by inserting an adjoining string and considering the tension that arises when the string is pulled taut by the centrifugal force. The planetary orbital example serves as the best all round general illustration of the subject of the article. So why not tell everybody what your real reason is for objecting to this example. Saying that it is a special case is not going to wash.

It seems from your edits above that you are somewhat puzzled as to how Leibniz arrived at the inverse cube law formula for centrifugal force. You say that you have never seen how Leibniz derived it. Neither have I, and I would indeed like to see how Leibniz derived it. I have seen some modern textbooks deriving it using some dubious method in which the total radial force in polar coordinates is reversed in, and the convective term, which had been a centripetal force in the polar coordinates in isolation, suddenly becomes a centrifugal force when gravity is involved. This is clearly not satisfactory and it amounts somewhat to 'force fitting', but it yields the correct end result. And so I agree with you that it would be very interesting to find out how exactly Leibniz derived it in the first place. This is not the only case in physics where a considerable degree of mystery hangs over the derivation of a very important result, and where the result itself is not in dispute. Maxwell's displacement current springs to mind. Few people doubt the authenticity of Maxwell's displacement current. But even fewer people can ever derive it without raising question marks. Not even Maxwell's own derivation is free from question marks. The amazing thing is that the end result is not only correct, but it is one of the most important results in modern physics along with perhaps the Leibniz equation which you are so keen to hide. David Tombe (talk) 17:02, 12 July 2009 (UTC)

You're a bit confused here. The 3rd viewpoint, the Lagrangian, was introduced by Brews, not by F. It's just a generalization to other things called centrifugal force that are like the CF that arises from coordinates measurements that don't correspond to coordinates in inertial reference frames; it effectively includes the rotating frame approach, by a different mathematical route. As to your statement that "Planetary orbits expose the outward force that is generated due to transverse motion," we think you're delusional; there's no such force in an inertial frame; your F=ma equation only gets such an F when you take "a" to be the second derivative or r, which is the coordinate measured along the co-rotating r-hat unit vector – a rotating reference frame. As I mentioned before, I think we can discuss the equation in the section on rotating frames; F has provided detailed sourcing for this interpretation, which he quoted above. If you will agree it's OK, then I'll encourage F to put it in, or I'll put it in. But if you insist it doesn't belong there, we're better off just leaving it out. Dicklyon (talk) 17:31, 12 July 2009 (UTC)

Dick, I'm not the one who is confused. There is only one centrifugal force. A rotating frame of reference is only needed when the physical scenario dictates. Examples are the rotating Earth and co-rotating atmosphere, and rotating turntables where dragging forces are involved which react against the already existing inertial forces.

When you are clear on this point, we will be agreed that the centrifugal force in such a co-rotaing scenario is the one and only centrifugal force that is described by either Lagrangian or polar coordinates.

Planetary orbits can be treated using rotating frames of reference, but it is not necessary to do so and it is indeed rare to see it done that way. I know that you have produced sources which do it that way, but most textbooks don't do it that way. I did the course many years ago and I checked out many textbooks for different ways of solving the planetary orbital equation. I never saw a book that used rotating frames of reference in this topic. So you cannot put a topic under the banner of 'rotating frames of reference' when it does not generally speaking fit under that banner. By all means support FyzixFighter and keep the planetary orbital topic out of the article altogether. But if you do so, you are merely indulging in a cheap numbers game at the expense of the reader. You will be deciding that anybody who googles up centrifugal force and inevitably gets led to the wikipedia article should not be allowed to read about the role of centrifugal force in planetary orbits, simply because you decided to side with FyzixFighter who has been actively and repeatedly deleting constructive edits that I make to physics articles. You have shown a capability of understanding these issues. But you have also shown a tendency to side up with other editors and work against your better instincts. You should be able to see by now that FyzixFighter's departure from his other edits to physics articles has been, not for the purposes of improving the articles in question, but for the sole purpose of undoing what I have just done. If wikipedia can't deal with that kind of subtle vanadalism then it will eventually become viewed with cynicism by the wider readership. David Tombe (talk) 17:49, 12 July 2009 (UTC)

How can you say there is only one centrifugal force? Read the article. Look at the table. Two different things going by the same name, acting of different objects, and not equal in magnitude except in the case of circular motion. You've had well over a year to find support for your POV, but it hasn't happened. Whether you arrive at your equation by Lagrangian or other methods, it describes the pseudo force in a system with rotating r vector, not a real force in an inertial system. Dicklyon (talk) 22:45, 12 July 2009 (UTC)

OK then Dick, you give me an example of centrifugal force that is exclusively one kind as opposed to the other. And while you're at it, can you tell me if the centrifugal force in the rotating bucket is the reactive centrifugal force or the 'rotating frames' centrifugal force? I remember you once tried to tell me that the centrifugal force in the planetary orbit was the reactive centrifugal force. And indeed there are some sources which back up that idea. But recently you have been wanting to put it into the 'rotating frames' section. FyzixFighter tried to bury the planetary orbital centrifugal force right in the middle of the Lagrangian section and now he wants to put it into the 'rotating frames' article.

So, I'll be interested to hear the example that you give me which is exclusively one kind of centrifugal force as opposed to another. I'll bet that what ever example you produce, I will be able to expose it as the one and only centrifugal force which is the inverse cube law force in the Leibniz equation. David Tombe (talk) 23:19, 12 July 2009 (UTC)

In any inertial-frame analysis, bucket or otherwise, the real forces are exclusively the centripetal force and the corresponding reactive centrifugal force. The other centrifugal force only comes up only as an apparent force in rotating reference frames. This is well known; you seem to be unique in not admitting that this is standard physics. Dicklyon (talk) 05:28, 13 July 2009 (UTC)

OK Dick, so you are saying that the water in the rotating bucket that pushes against the edge of the bucket is the 'reactive centrifugal force' and measured relative to the inertial frame. And no doubt it will satisfy the polar coordinate term for centrifugal force as referenced from the centre of rotation. And no doubt it will obey an inverse cube law when angular momentum is conserved. And no doubt if we should so choose to involve a rotating frame of reference, it will be the associated centrifugal force in the rotating frame. And this reactive centrifugal force will no doubt correspond to the centrifugal force that arises if we analyze the problem using Lagrangian mechanics or if we analyze the problem using the concept of centrifugal potential energy.

You haven't convinced me that there is more than one centrifugal force involved. David Tombe (talk) 08:02, 13 July 2009 (UTC)

FyzixFighter Reinvents Physics

As far as I can see this fellow FyzixFighter appears to advocating a revisionist physics. If you want to reinvent physics to fit your own views of the world, I dont think you should do it here. The idea that centrifugal force keeps planets in their orbits is a central idea of modern physics. I remember being taught that in the school books. Apparently you didnt read them or didn't understand the point. If there is no centrifugal force, the planets fall into the sun. Is that not obvious to you? Apparnetly this discussion has become so embroiled in personal nastiness on your part that such obvious facts are being overlooked. If there is no centrifugal force keeping the planests from falling into the sun, please explain what does, Mr FizixFighter, and please dont invent any new physics or appeal to any obscure sources. Just give us a simple reason that can be understood that justifies why you are creating this unnecessary edit war.72.84.73.235 (talk) 14:27, 13 July 2009 (UTC)

That's not exactly the modern view. All you need to keep planets from falling into the sun is inertia, via Newton's law F=ma, with the only force being the force of gravity. Physics was "reinvented" this way by Newton a long time ago. Dicklyon (talk) 14:51, 13 July 2009 (UTC)

I was just about to say much the same thing. Gravity stops the planets from flying off in a straight line.Martin Hogbin (talk) 14:54, 13 July 2009 (UTC)

User talk:72.84.73.235: You are not wrong in your statements; it's all a question of frame of reference: Dicklyon and Martin Hogbin use an inertial frame; you (perhaps unconsciously) use the frame of reference of the planet. The planet is at rest in the frame of the planet because the centrifugal force and the force of gravity balance. The most natural frame of reference, the one instinctively adopted in an amusement park ride or a turning car, is the frame attached to the body. Brews ohare (talk) 15:12, 13 July 2009 (UTC)

Centrifugal force is due to inertia. So you can't deny centrifugal force on the grounds that it is the effects of inertia. 72.84.73.235 is using the language of centrifugal force. And that's what this article is about. You can't veto the most important example of centrifugal force on the grounds of switching language to Newton's law of inertia. And we all know that Newton had a chip on his shoulder because Leibniz got to the inverse cube law before him, and so Newton played down centrifugal force in his later works. David Tombe (talk) 15:18, 13 July 2009 (UTC)

I'm not denying centrifugal force, or the fact that it's due to inertia. I agree it is. But in the inertial frame, it's not a force; what balances the F on the left of F=ma is the ma on the right; this is how Newton incorporates inertial effects in inertial frames. Dicklyon (talk) 18:02, 13 July 2009 (UTC)

Really!? I'm using obscure sources? I'm appealing to the same sources that David first inserted into the article, namely Linton's "From Exodus to Einstein" and Swetz's "Learn from the Masters!". Both of which support the idea that the centrifugal force, more specifically Leibniz's centrifugal force, is absent in the inertial frame. See page 264 in Linton, and near the top of page 269 in Swetz. I've listed the full quotes in a section above, so I won't belabor the other editors by posting them again. If those are obscure sources, then you better get on David's case too for bringing them up in the first place. --FyzixFighter (talk) 15:40, 13 July 2009 (UTC)

FyzixFighter, the sources which I inserted were for the purpose of backing up my assertion that the centrifugal force is an outward inverse cube law force. It is neither here nor there what additional opinions the authors held on the matter. You have just deleted a section which states that the centrifugal force is an outward radial force which obeys the inverse cube law. Your reason for doing so does not match your determination. Why would anybody be prepared to have an edit war on this issue simply on the grounds that they don't think that the section is necessary? You removed that section for the sole reason that you have got a chip on your shoulder. It has got nothing to do with any arguments in physics. And you are taking advantage of a hostile environment of editors who are paranoid about centrifugal force because of the threat which it poses to their favourite theory of relativity. We're seeing an example of it right now as regards the latest objections to the 'absolute rotation' section. In fact, I strongly suspect that you yourself began this edit war for this very reason when you first noticed in April 2008 that I had edited on this page to state that centrifugal force is the radially outward force that arises in connection with mutual transverse motion. You have never declared your motives so far. You are playing out a clever little game of pretending to be merely interested in ensuring that wikipedia's rules and regulations about sources are being upheld. And you know exactly how to use the wide range of contradictory sources to mess the article up. Why would somebody who normally edits on non-physics articles be so keen to ensure that sources are being correctly used on the centrifugal force page and then proceed to delete material that has been fully sourced? David Tombe (talk) 21:04, 13 July 2009 (UTC)

What is the purpose of this article?

What is the purpose of this article? I we cannot all agree on this it is going to be hard to agree on the wording.

Is it:

1) A form of disambiguation page to direct readers to the appropriate article to meet their needs.

2) A list of all the different ways in which the term 'centrifugal force' has been used, with some discussion of each.

3) Something else. Martin Hogbin (talk) 17:09, 13 July 2009 (UTC)

I'd say 2. More than a disambig, but a WP:Summary style article. Dicklyon (talk) 17:59, 13 July 2009 (UTC)

I agree with Dick - #2, covering the different ways the term has been and is being used. One section that I'm having trouble seeing fit into that scheme is the current "absolute rotation" section. But maybe once we agree on the purpose, we can discuss that concern more directly. --FyzixFighter (talk) 19:06, 13 July 2009 (UTC)

I agree that the 'absolute rotation' section does not fit in at all. Why not remove it then? Martin Hogbin (talk) 20:02, 13 July 2009 (UTC)

The section was copied in from another article on 13 May by David Tombe in this diff with summary (bringing across interesting section from the branch article. But it needs to be drastically reduced in size). I questioned it in this talk diff; see Brews and David followups. Brews seems to share some concern about the section relative to the purpose of the article, but decided to side with David and expand it. These two guys tend to be on opposite ends of most arguments, and their disagreements invariably lead to article bloat, as in the centrifugal force (rotating reference frame) article that we're trying to avoid duplicating here, which is where it was imported from. I agree we should either get rid of or greatly reduce this section; maybe even make a whole article on this interesting topic, which is pretty off topic for a summary article. Dicklyon (talk) 16:55, 14 July 2009 (UTC)

Well of course Martin, at the end of the day it is 'absolute rotation' that is the thorn in the neck for relativists, and so from your perspective it would be better that such a section should not be seen. I can see from your intervention here that you are very keen in singularly promoting the 'rotating frames of reference' approach as being the only legitimate approach, and so you want to scotch all aspects of centrifugal force that don't sit comfortably with your preferred approach. You clearly don't like the idea that absolute rotation causes pressure in the water in a bucket. This is of course an article about centrifugal force, but you obviously want all the readers to be taught that centrifugal force is merely an illusion that arises when observations are made from a rotating frame of reference. I don't support your idea to remove that section. But I doubt if my viewpoint will get majority support in this arena. David Tombe (talk) 20:17, 13 July 2009 (UTC)

Absolute rotation: I don't see why the article has to have a single purpose: usages of the term. It also has the purpose of introducing articles of interest to centrifugal force. Certainly the history is is one such. Absolute rotation is another, inasmuch as this plays a key role in the history and in the applications. It also is key to understanding the difference between inertial and noninertial frames, the origins of general relativity, and the distinction from the Lagrangian approach. All these sections refer the reader to other WP articles likely to be of interest. I do not think a person looking up centrifugal force here is looking for a dictionary: they may have other interests and simply chose "centrifugal force" as an entry point hoping to find what they really are looking for. Brews ohare (talk) 20:35, 13 July 2009 (UTC)

As I was the one who brought this up, maybe I should elucidate a bit. I could see including it as a subsection of the historical part. What is the current status of the absolute rotation debate? The first two parts, the bucket argument and rotating spheres seem to me to be directly tied to the early debates about absolute rotation. (These parts also make parts of the detailed "see also" section redundant). I don't see how the third section enters in the absolute rotation debate; I see it more as a historically interesting application of the centrifugal force concept. In other words, the references provided do not establish that the oblateness of the earth entered into the absolute rotation debate like the other two parts do. --FyzixFighter (talk) 21:06, 13 July 2009 (UTC)

FyzixFighter, that's all shear sophism. Nobody could possibly follow your point. Basically you want 'absolute rotation' off the page for the same reason that you wanted the planetary orbital equation off the page. You want to erase all evidence that centrifugal force is associated with a real pressure. You've got centrifugal force as an inverse cube law force off the page. Now your target is 'absolute rotation'. Next it will be the Lagrangian section. Finally it will be the 'reactive centrifugal force'. Then you will feel that you have successfully fought to make physics pure and relativistic. You will have a nice clean article based on solid relativistic values. David Tombe (talk) 21:13, 13 July 2009 (UTC)

I support removing the section entirely; it's already in the "main" article that we link to on rotating reference frames; let's get back to summary style, and move these debates to the relevant pages. Dicklyon (talk) 16:56, 14 July 2009 (UTC)

Dick, I agree with your earlier proposal that this section should be reduced in size. In fact, if you examine the edits carefully from May 2009, you will see that I made this very point myself. I said that this section should ideally be drastically reduced in size. I even made suggestions as to which key points should be left in. I gave Brews a rough sketch of a derivation for the centrifugal potential energy equation. Interestingly, it was originally in the rotating frames re-direct article. But it straddles all kinds of centrifugal force. Hence we need a summary of it in this summary article. David Tombe (talk) 18:29, 14 July 2009 (UTC)

I agree with Dick, remove it completely, it is different subject. Martin Hogbin (talk) 13:53, 15 July 2009 (UTC)

Consensus on the Planetary Orbital Topic

Once again, FyzixFighter has removed the section on planetary orbits and left no part of the article, apart from the history section, to explain the fact that centrifugal force is an inverse cube law force. And in doing so, FyzixFighter claims that he has got consensus on his side.

Let's examine that consensus. I initiated the section as the most general illustration of centrifugal force. FyzixFighter immediately came along and deleted it. Brews re-worded the section and re-inserted it. FyzixFighter deleted it again.

The final analysis is that Dick was initially disinterested in the edit, but as usual supported FyzixFighter when it came to the crunch. However Dick didn't actually object to the content of the edit as such. He agreed that the edit could be put into the re-direct article 'centrifugal force (rotating frames of reference). But the problem with that is that planetary orbits are not normally dealt with in connection with rotating frames of reference, and so it would be totally inappropriate to put the planetary orbit section into the re-direct article about rotating frames of reference.

Anonymous 72-- -- -- restored the section. Wolfkeeper's popup mechanism automatically undid 72's edit within minutes. I don't count Wolfkeeper's popup mechanism in relation to anything to do with consensus on this issue because he hasn't been involved in the debate.

So the evidence is that myself, Brews, and 72 are in favour of the edit. Dick is ambiguous in that he is comfortable enough with the edit providing that it doesn't appear on the correct page. So I very much doubt that consensus on balance can be said to be in favour of FyzixFighter's desire to delete the edit.

Here we have a situation where FyzixFighter, who only concerns himself with the centrifugal force page when I have made an edit, comes along and deletes such an edit on the very weak grounds that the content matter is a special case of centrifugal force, and that as such he doesn't think that it should appear in the article. And he is prepared to have an edit war over the issue.

It is because of the likes of FyzixFighter that it is impossible to work constructively to improve this article.

The question is, 'where do we now mention the inverse cube law relationship in this article? Do we mention it in the introduction or do we write a special section to say that Leibniz demonstrated that the centrifugal force obeys an inverse cube law relationship in the radial distance?'. It's currently mentioned in the history section but it is still very much a part of modern physics. David Tombe (talk) 19:34, 13 July 2009 (UTC)

David, why are you so keen to mention the inverse cube relationship? It is there, but only if angular momentum is constant, for example a particle in a central force field. Is it perhaps because you have your own theory on the subject? This is a quote from an abstract of your theory, 'It is widely believed that centrifugal force does not exist. It will now be shown that centrifugal force is a dipole force field comprising of a sea of tiny rotating electron-positron dipoles which constitutes the luminiferous medium. Centrifugal force is the inverse cube law repulsion that emanates from the net positive charge that is generated in the dipoles when they are subjected to certain kinds of forces'. Martin Hogbin (talk) 21:09, 13 July 2009 (UTC)

Martin, yes. I'm glad you understand that. Few others do. Conservation of angular momentum leads to an equation which can be substituted into the centrifugal force expression to make it into an inverse cube law relationship. My objective here is to help others to learn about centrifugal force. I edit on pages about topics that I have a particular interest in. That's what wikipedia is all about. The centrifugal force page is there for people to learn about centrifugal force. I have been trying to create a simplified and coherent article with all the important aspects and with the most general illustrations. The two body problem is the singular best illustration, because ideally we can't ignore the gravitational field. If however we do ignore the gravitational field, and consider the random motion of two objects, we will find that this motion can be resolved into a translational motion of the centre of mass and a rotation about the centre of mass. Hence, centrifugal force is a real radial force that is related to inertial mass because the inertial mass will determine the actual centrifugal acceleration relative to the common centre of mass. This is confirmed when we attach a string between the two objects. The string will go taut, due to centrifugal force, and the two objects will perform circular motion about the common centre of mass.

My question to you is, 'why would we want to hide the inverse cube law fact from the readers?'. What aspects of centrifugal force would you see as being the most important and most interesting? David Tombe (talk) 21:25, 13 July 2009 (UTC)

I do not want to hide anything but the inverse cube law is more a property of a central force. For example I could equally well say that centrifugal force is constant (for a fixed length string) or that it is zero (for motion in a straight line). Centrifugal force is about motion in a circle and the essential variables are velocity and radius. With just these two there is no inverse cube law, that it a property of a constant angular momentum system. Martin Hogbin (talk) 21:55, 13 July 2009 (UTC)

I think it's worth mentioning, too, as it's an important application of the concept of CF to planetary orbits. I just don't think we can accommodate David's interpretation of it as different from the usual pseudo-force due to the rotation of the direction along which the coordinate r is measured. Dicklyon (talk) 22:12, 13 July 2009 (UTC)

You have seen the reason that David is so keen on this! The inverse cube law only applies to a specific application CF, it is not a general result. Martin Hogbin (talk) 22:26, 13 July 2009 (UTC)

I have no idea why he's so keen on it, but I agree it is a rather narrow application. But it's an important one, both historically and even for modern orbit calculations, and as an illustration of how CF can be derived and applied. His deep confusion about it, shared now and then by an anon who supports him, suggests that it is worth treating carefully and correctly. Dicklyon (talk) 22:34, 13 July 2009 (UTC)

I am not suggesting that it is not an important application (although the two body problem is rarely treated using centrifugal force) but noting that it is just that, an application. The inverse cube law is more part of the application than a property of the force itself. Martin Hogbin (talk) 22:55, 13 July 2009 (UTC)

Carfeul here, the inverse cube law is the most general case. Circular motion on the end of a string involves a fixed radius and that is only a special case. Martin seems to think that centrifugal force is something that only arises in circular motion. That is a common error. Centrifugal force arises in the inertial path, and the inertial path is in general a conic section with the centrifugal force being a variable inverse cube law quantity. One special case of the inertial path is a straight line motion in the case of zero gravity.

And Dick, I was never saying that the centrifugal force in planetary orbits was a different concept from other centrifugal forces. In fact, I have been consistently saying that there is only one centrifugal force. I drew your attention to the rotating bucket of water and showed how there is only one centrifugal force. That very same inverse cube law force in the inertial path pushes the water to the sides. It causes the centrifugal potential energy in the water and it causes the push on the sides that you would classify as the reactive centrifugal force. I am still waiting to hear your comments on that. David Tombe (talk) 13:09, 14 July 2009 (UTC)

David, I'll repeat my comments. In the planetary orbit, the centrifugal reaction force is the equal and opposite force that the planet exerts on the sun, with reciprocal-r-squared dependence, because it is just gravity; the pseudo-force CF is reciprocal-r-cube. In a circular orbit they are equal, or in balance (for the right value of angular momentum for that orbital radius). But in general they differ, because they are completely different things. Same way for a weight on a string or a bucket of water; the two concepts of CF are equal only in circular motion; they are not at all the same thing. Dicklyon (talk) 02:35, 14 July 2009 (UTC)

And the reason that I am so interested in the Leibniz equation (not knowing until recently, thanks to you, that it was actually Leibniz's equation) is because it so perfectly embodies everything to do with this topic, plus more. It contrasts the two opposing central forces with their respective inverse square laws and inverse cube laws. The two different power laws yield the stability node which makes planetary orbits stable. If perchance we happened to have inverse cube law gravity, then the planets would spiral into the Sun. The stability node gives a picture of elliptical planetary orbits as like a two dimensional spring that is stretching and compressing, and it clearly illustrates gravity as a 'pull' or tension, and centrifugal force as a 'push' or pressure.

That's just nuts; there are not two different central forces – just gravity. The other is a made up pseudo force to allow you to pretend that you have a one-dimensional problem in r; that's all. Not very fundamental, really. Dicklyon (talk) 02:35, 14 July 2009 (UTC)

It's an interesting subject and I don't see why attempts to present it clearly and concisely have met with so much opposition. David Tombe (talk) 00:21, 14 July 2009 (UTC)

The reason is that you insist on presenting it as something that it's not, in contrast to the many sources, none of which support you in this. Dicklyon (talk) 02:35, 14 July 2009 (UTC)

Dick, it was actually Brews who wrote the deleted section, and I fully support the way that he wrote it. Can you please elaborate on exactly how it presents the centrifugal force as something that it is not. At any rate I have a compromise idea that will involve a short introduction section pointing out the key historical points in the evolution of the modern ideas. David Tombe (talk) 11:57, 14 July 2009 (UTC)

Suggestions

For what it is worth I have added an 'oppose' comment to the RfC section regarding the Leibniz inverse cube statement.

I have also put the 'Fictitious force' section first in the article as it is the one most used in physics today. I appreciate that the other definition may still be current in engineering but I suspect that this is in a relatively informal context. Anyway, all I have done is changed the order.

The section on absolute motion does not, in my opinion, belong here, especially if this article is intended to be a summary of centrifugal force. I suggest that it is removed completely.

Martin Hogbin (talk) 09:04, 14 July 2009 (UTC)

Martin, an article is an article. This is an article on centrifugal force. I don't know where the idea of it being a 'summary article' stems from. There are indeed two re-direct articles, but there are aspects of centrifugal force which either straddle the two re-direct topics or don't accurately fit into either of them. Where do you suggest that we put such topics? The absolute rotation section is one such example. The rotating water in the bucket involves all aspects of centrifugal force. It can be analyzed using rotating frames or using the inertial frame, and it involves centrifugal potential energy as well as pressure on the walls of the container. Dick said yesterday that it was a 'reactive force' topic, but I am waiting to hear his comments on the fact that the inertial force acts in the water itself as well as against the wall of the container. David Tombe (talk) 13:06, 14 July 2009 (UTC)

There are many interesting applications of centrifugal force but we do not want them all here. The absolute motion section is really all about Mach's principle. If we have a section on a different but related subject we could also have sections on centrifuges, turbine blades, fairground rides, cyclotrons etc. Martin Hogbin (talk) 13:18, 14 July 2009 (UTC)

Martin, and why do we not want all those topics to be in a centrifugal force article? David Tombe (talk) 13:24, 14 July 2009 (UTC)

Because, if we decribed every related topic in every article, WP would be cumbersome and unusable. Martin Hogbin (talk) 13:39, 14 July 2009 (UTC)

Reasons to support the absolute rotation section have been stated here. Brews ohare (talk) 20:05, 14 July 2009 (UTC)

History articles in general

There are times when a history section rightfully belongs at the bottom of an article. That would be in the case when there is a long chronology of obselete ideas, such as with the history of the periodic table. But there are other occasions in which the modern day understanding of a topic is very closely tied to its historical evolution. And if that topic remains ambiguous in the present day literature, it is very important that a brief historical lead in to the topic appears early in the article.

The current confusion over the reactive centrifugal force concept can't be fully understood in the absence of a mention of Leibniz's equation. And Leibniz's equation is still used today in planetary orbital theory, and so it is not entirely history.

The story is that Leibniz produced the planetary orbital equation which included the inverse cube law centrifugal force. Newton objected to that equation and claimed that centrifugal force is an equal and opposite reaction to the centripetal force.

The problem that we have here is that the most common modern approach to centrifugal force as a topic in its own right is neither the Leibniz approach, nor the Newtonian approach. On the other hand the modern approach to planetary orbits cannot be done in the absence of centrifugal force even though there has been a remarkable dilution in recent years as regards explicit mention of that fact.

The matter is further complicated by the fact that there is even a divergence as regards what the reactive approach actually entails. Some texts cite the reactive approach exactly as per Newton, acting on the same body as the centripetal force, and even apply it to planetary motion. Other texts look at the transmitted knock on effect which this centrifugal has on another body and try to reconcile it all in terms of Newton's third law of motion over two bodies.

For a compromise, we need to have a short introduction to the article which points out these important points. What follows next in the main sections will depend entirely on which editors decide to write more on their particular area of interest. David Tombe (talk) 11:54, 14 July 2009 (UTC)

Leibniz was an excellent mathematician but his concept of centrifugal force plays no part whatsoever in modern physics. His assumed inverse cube law happens to be the case for a particle in a central force field but his theory is of historical interest only. Martin Hogbin (talk) 13:37, 14 July 2009 (UTC)

Martin, how can it be of historical interest only if it is still used today. I used it at university. It is in my applied maths notes. It is equation 3-12 in Goldstein's 'Classical Mechanics'. This is one of these situations where the historical evolution and the dispute with Newton forms a necessary lead in to the differeing approaches to centrifugal force that appear in the modern textbooks. You cannot hope to explain the reactive concept (in either form) without some reference to the story of Newton's reaction to Leibniz's equation. In fact. I'll show you this reference so that you can read about it. See here David Tombe (talk) 16:32, 14 July 2009 (UTC)

The current sources (such as Aiton, Swetz, and Linton) that address Leibniz and his role in the history of the centrifugal force are also clear that his description of the dynamics is tied to the co-rotating, non-inertial frame. All modern sources that get the planetary orbit equation or something similar get there via Newton's laws and non-inertial frames or Lagrangian mechanics and generalized forces. --FyzixFighter (talk) 14:43, 14 July 2009 (UTC)

FyzixFighter, my intention was to fully address that issue. I am looking for a compromise. I had every intention of mentioning the fact that most modern textbooks introduce centrifugal force in connection with rotating frames of reference. However, planetary orbital theory is not in general treated using rotating frames of reference even if there are exceptions such as you have cited.

My planned wording was going to finish something along the lines of what I have just said. Ie. " Subsequent to the time of Leibniz, the concept of a rotating frame of reference became gradually more prevailent in physics. That concept features prominently in the important works of Gustave Coriolis (1835) and nowadays it is the most common context in which the centrifugal force is introduced - - - ".

I think that this would be a fair compromise. The next section could then deal specifically with centrifugal force in rotating frames of reference. David Tombe (talk) 16:19, 14 July 2009 (UTC)

I think it could be mentioned in the history section in some such way (maybe it is already, I'll have to review); but be sure to say it in a way that you can back up with a source; and we don't really need the equation in the history. Dicklyon (talk) 16:59, 14 July 2009 (UTC)

Dick, I've put in a short introduction. It duplicates material from the history section, but the particular aspects of history in question are important for the purposes of leading in the subject. If that introduction is acceptable, then the edit war is over. Discussions may continue, but the edit war will be over because the controversial material will have been given its due place, albeit in a very much watered down manner from what I would have preferred. David Tombe (talk) 19:40, 14 July 2009 (UTC)

Dick is correct that sourced and non-OR bits of your "compromise" introduction are already in the history section. If stating the history is important to leading into the subject, then I would suggest moving the history section to earlier in the article. But I think the modern science understanding is the best way to lead into the article. What do others think, do we need a detailed history/intro section? --FyzixFighter (talk) 21:58, 14 July 2009 (UTC)

David's proposed introduction

Sir Isaac Newton said that centrifugal force is the equal and opposite reaction to a centripetal force as per his third law of motion. However, the circumstances in which Newton made this conclusion need to be carefully considered. Newton was responding to the planetary orbital equation which had been derived by his arch rival Gottfried Leibniz. Leibniz's equation indicated that centrifugal force is a radially outward force that obeys the inverse cube law in the radial distance. Leibniz's idea contradicts Newton's concept of centrifugal force in that in Leibniz's view, the centrifugal force does not have to be equal in magnitude to the centripetal force. It is believed that Newton was once working on a similar approach to Leibniz but that he adopted this contradictory stance on first seeing Leibniz's equation for the sole purpose of denigrating Leibniz's work. Both of these approaches to centrifugal force are still found in the literature today. The Leibniz approach is still the basis for solving the two body central force problem, albeit that explicit references to the centrifugal force term in this context are becoming increasingly diluted in the literature. Meanwhile, the Newtonian approach is also rapidly disappearing from the textbooks.

The most common approach to centrifugal force in modern textbooks uses the concept of rotating frames of reference. The concept of rotating frames of reference began to arise in physics in the 18th century and this concept features prominently in an important paper written in 1835 by Gustave-Gaspard Coriolis. Centrifugal force is nowadays considered to be a fictitious or an inertial force which arises when a situation is viewed from a rotating frame of reference.

Discussion

As I stated before, this is pretty well covered already in the history section. However, there are several points where this text is lacking and OR:

1. First line about Isaac Newton - actually Newton totally dropped the idea of centrifugal force in his Principia (see Linton, pg 264). Only when he started arguing with Leibniz did Newton make this argument and mis-applied his 3rd law. As Swetz notes, Newton and Leibniz were using the term centrifugal force in different senses.
2. "...need to be carefully considered." - POV and unsourced editorializing.
3. Leibniz's approach description - fails to mention that he was working in a rotating frame (see both Swetz 269, and various parts of the Aiton paper)
4. "...increasingly diluted in the literature...rapidly disappearing from textbooks" - completely unsourced opinion
5. Second paragraph, again already covered in the history section

As I stated above, if we want a section like this at the beginning of the article, let's move the history section up. However, I think the history section works better after the extremely mainstream summary explanations. --FyzixFighter (talk) 21:58, 14 July 2009 (UTC)

Personally, I usually prefer a history section early, to help position the concepts. I haven't determined whether that is necessarily better in this article, but it might be. Dicklyon (talk) 22:08, 14 July 2009 (UTC)

FyzixFighter, I appreciate that certain items are duplicated in the history section. But my intention here was to highlight the key historical aspects which most directly lead into the concepts in modern usage. If we can sort the introduction out first, then we can tidy up the history section afterwards. Like I explained earlier, there are times when it is best to have a history section early, and there are times when it is best to have it later. A lengthy history section is best at the end of an article.

As regards rotating frames of reference, that issue was adequately dealt with. I clearly stated that the idea crept in and took root as early as Coriolis's 1835 paper. Leibniz himself didn't use the concept. We cannot retrospectively impose the concept unto the Leibniz approach simply because modern authors who were writing about him stated their own opinions on how they thought it should have been, based on the paradigms of the era that we now live in. I think that you are going over the top a bit on this rotating frames issue. You are using sources disproportionately. The majority of textbooks on planetary orbital theory do not use rotating frames of reference. It is therefore quite wrong to describe the historical Leibniz equation in that context. I stated the Leibniz approach and the Newtonian approach and then went on to point out that we then moved into an era of rotating frames of reference. It that not a sufficient compromise? Don't forget that we are trying to get a compromise to end the edit war. This is instead of having a full section on the two body problem with equations. David Tombe (talk) 23:40, 14 July 2009 (UTC)

Then let's fix up the history section and move it earlier in the article. Honestly IMO the history section is pretty good, though it jumps around a bit at the beginning - I'll see what I can do on that. I'm not in favor of moving it up, but if most of the editors feel that it belongs at the beginning of the article then that's what we'll do. Thoughts Martin and Brews? Moving it for me it's a flow/aesthetic issue and not a content issue.

As for going over the top with casting Leibniz in the rotating frame paradigm, unfortunately all of the historical references we have that talk about Leibniz do this. Do you have a reference that talks about Leibniz and doesn't talk about rotating frames?

I'm highly skeptical of your statement that the majority of textbooks on planetary orbital theory do not use rotating frames of references. The only instant where they would not is if they are using Lagrangian mechanics (such as Goldstein and Shankar), in which case it highlights the distinction between a Newtonian force and a generalized force and the Lagrangian section covers those instances. If they are using Newtonian mechanics, using F=ma, to get the radial equation then they are using rotating frames. In Newtonian mechanics, centrifugal forces do not appear on the force side of F=ma for planetary orbits; to paraphrase Linton, Leibniz's centrifugal force disappears in Newton's Principia, it's not needed, only a centripetal forces exist.

Read Aiton's article. He does a good assessment and analysis of Leibniz's derivation. Leibniz had the brilliant idea to cast his problem by only considering motion along the rotating radius vector, in modern parlance Leibniz was describing his dynamics in a rotating reference frame (as Aiton clearly indicates multiple times). When Leibniz was considering motion along the rotating radius vector, he found that Kepler's laws leads to a radial equation of the form that we are all familiar with, r-double-dot on one side and a negative inverse square term and a positive inverse cube term on the other side. We agree that the equation is mathematically valid. But the question that sums up our disagreement is whether Leibniz's early concept of centrifugal force can be interpreted meaningfully. The answer according to all the secondary sources is this: in the inertial frame, considered as a force (using the traditional since the days of Newton definition of force) acting on the circulating body itself, his centrifugal force does not exist (see Swetz, pg. 269). Only in a reference frame rotating with the circulating body does the body appear to have an endeavor to recede from the center (again, Swetz, pg 269). I don't see how we can write anything else without being true to the sources. Is there anyone besides David that disagrees with this summation? Are there any sources that disagree with this? --FyzixFighter (talk) 03:19, 15 July 2009 (UTC)

FyzixFighter, It's more the case that I agree with Leibniz's interpretation as you have described it above. I see it in that exact same way. We have a radial equation with two radial forces. And I can assure you that in 1979/80, I never once saw a textbook that dealt with planetary orbits any other way, although, as I said in the edit, explicit references to the word 'centrifugal force' were rare. I originally did the course using Williams's 'Dynamics'. It contained the relevant equation and it didn't use rotating frames of reference. But equally, there was no explicit reference to the word 'centrifugal force' in relation to the corresponding term that Leibniz would have called centrifugal force. The book I used the next year was Goldstein. I didn't do planetary orbital theory from Goldstein. We used that book for 'Lagrangian mechanics'. Nevertheless, the same equation appears in the planetary orbit chapter of that book, and Goldstein does call the term 'centrifugal force'. However, his use of the term leaves the application somewhat ambiguous and hence leaves the situation open for some, such as yourself and Dick, to claim that he was only using the term in connection with the equivalent one-dimensional fictitious problem. On the other hand it is also obvious that the term when written in the form that uses angular speed, can only be referring to equation 3-12 which is written in relation to the real two dimensional problem. That's what I meant when I said that explicit references to centrifugal force in the context have become increasingly diluted. I could even give you the comparative quote between pages 176-179 as between the two editions of Goldstein (1980 v. 2002) to illustrate the changing attitudes. Likewise, I could show you the comparative quotes in Nelkon & Parker as between 1961 and 1970 which also show the corresponding changing attitudes to the Newtonian concept in our times.

So if we are going to mention the Leibniz equation, then we should mention it without imposing what some authors consider to be the modern interpretation of it. The correct balance is to state Leibniz's position and then state that the move then drifted towards rotating frames of reference, and that modern textbooks mostly introduce centrifugal force within the context of rotating frames of reference. If you insist on connecting rotating frames of reference directly with the Leibniz equation, then you are indulging in revisionism and you are using sources selectively to back up your own point of view. Likewise if you claim that the Leibniz equation is purely historical, you are then denying the truth that it is still very much used today, irrespective of the differing interpretations that are found throughout the literature. There is a way of writing these complex issues in a truthful and balanced matter which is in line with the sources.

You on the other hand are using sources in a manner such as to impose a modern viewpoint on top of a historical viewpoint. It's known as re-writing history. The bottom line is that I think that Leibniz was right (apart from his solar vortex model) because it's the only way that you can treat the centrifugal force between mutual pairs of objects in a three body problem or upwards. The rotating frames approach only considers one sigle angular speed and it ignores the individual centrifugal forces between any pair of particles in a multi particle system. That's why I have my point of view. But you haven't declared your motives for being so strongly opposed to the Leibniz point of view, and you are hiding behind selected sources claiming to be on the side of wikipedia's rules, when in actual fact, the situation regarding those rules leaves a considerable degree of leeway. That's why I have wanted the involvement of an administrator who is knowledgeable of the facts of the dispute. This dispute cannot be allowed to be won on a head count of editors who know absolutely nothing about the topic.

As for the history section itself, I agree that it needs to be tidied up a bit. But what do you want to do to it? Do you want to re-write history by imposing the modern attitudes on rotating frames of reference on top of old ideas that didn't use such a concept? As far as I am concerned, it all went off the rails when Coriolis failed to see the physical link between the Coriolis force and the associated rotating frame of reference. But that is my opinion and I will not be writing that in the article. Likewise I would hope that you would equally show respect for viewpoints as they arose at the time in question, and also in relation to the differing viewpoints which exist even in the modern literature. We cannot allow history to be re-written by 'some' selected modern sources. David Tombe (talk) 11:09, 15 July 2009 (UTC)

Goldstein's planetary section is done using Lagrangian mechanics - so that source is covered by the Lagrangian section. Interestingly enough, when the mr*theta-dot^2 term appears on the left hand side, he calls it a centripetal acceleration term. Since all the reliable sources we currently have place Leibniz's derivation squarely in the rotating frame paradigm, that is how his scheme will be presented, both historically and in how his radial equation is used today (at least when derived using F=ma). --FyzixFighter (talk) 13:43, 15 July 2009 (UTC)

FyzixFighter, Goldstein calls the radial convective term 'centripetal force' in connection with polar coordinates in the absence of a gravitational field. That has got absolutely nothing to do with the topic in question. In the planetary orbital equation, that same mathematical expression is unequivocally the centrifugal force. This is an example of you trying to distort the facts. Under no circumstances can the inverse cube law term in the Leibniz equation be the centripetal force. As regards the reversion which you did, the contents alone are not what was important. It was the manner in which the contents led the topic in. Your arguments for removing that material are totally barren. You are putting up an outward show of intellectual argument, but what you are saying is so badly wrong. You know the truth, but you are intent on twisting the facts. As I have said, you are merely playing a clever card game with sources which takes advantage of the confusion in the literature. You are using sources selectively to sabotage the overall understanding of the topic. David Tombe (talk) 13:59, 15 July 2009 (UTC)

Lagrangian centrifugal force

The suggestion has been made that the Centrifugal force#Lagrangian formulation of centrifugal force section is superfluous, or invented "to attract attention" to other articles (apparently connecting to other articles related to Centrifugal force is evil). However, I'd like to draw attention to long debates over "curvilinear centrifugal force" that involved editors SCZenz, Paulo.dL, Rracecarr, PeR, Wolfkeeper, TimothyRias, FyzixFighter. Tstone T, Fugal which involved the notion that Newton's concepts were at a minimum antiquated and probably wrong, that everything depended upon the metric of the coordinate system chosen and that centrifugal force that was zero in Cartesian coordinates suddenly showed up in polar coordinates. The way out of this round-robin was the Lagrangian formulation, which agreed with that viewpoint, but was historically understood in relation to the Newtonian formulation. Do you all really want to open that can of worms again? As soon as the Lagrangian formulation disappears, the whole cycle starts over again. And BTW, the Lagrangian formulation is (i) currently in active use, (ii) a topic of great importance & (iii) very well documented. Brews ohare (talk) 21:03, 14 July 2009 (UTC)

My short answer is no, let's not revisit it. The references provided that identify the Lagrangian centrifugal force as corresponding to the (q-dot)^2 terms in the generalized force are sufficient for me to demonstrate that it isn't superfluous and I think the current section adequately and accurately reports what's in the sources. The concept is certainly is not as prevalent in most common discussion and education settings, but the references show that it is significant and used by some (robotics as you've pointed out previously) today. The only thing that I would add is a line or two at the "redirect" from the fictitious CF section describing the "hand-waving" way of getting the Lagrangian CF in the simple, polar coordinate case from a Newtonian mechanics approach by moving the centripetal acceleration term to the other side and reinterpreting it as a "force", and of course the short disclaimer that by doing so the Newtonian definition of force has gone out the window. --FyzixFighter (talk) 21:22, 14 July 2009 (UTC)

Brews, the topic was new to me too. I had never heard of the Lagrangian approach to centrifugal force before. So in that respect, I learned something new, which is what wikipedia is all about. I was particularly interested in the bit where you showed that centrifugal force was i^2 whereas Coriolis force was i×j. Those simple products of the components of the coordinates provide a fascinating insight into the nature of the forces. The question then arises, what happens if we bring in a k? Do we have an axial Coriolis force with a jxk? David Tombe (talk) 21:37, 14 July 2009 (UTC)

FyzixFighter, you have often brought up the mystery of how the centripetal force in polar coordinates becomes a centrifugal force when it appears in the planetary orbital equation. I agree with you that this is a very interesting question. But it's an example of something that the textbooks are not going to solve for you. The answer ultimately lies in the fact that the inertial path can't be analyzed in the absence of a gravitational field. The modern textbooks 'force fit' the polar coordinate expressions to get the correct result in the radial planetary orbital equation. That of course opens up the minefield of terminologies. The modern textbooks like to use the term radial acceleration for the entire sum or r(double dot) and the centripetal term. These are the areas where all the controversy lies. But they can be glossed over in the article. David Tombe (talk) 21:44, 14 July 2009 (UTC)

It is not clear to me whether the terminology in which terms are referred to as centrifugal force is a generally accepted one or just what the authors chose to call those terms in their particular calculation. Can anyone give me evidence that this terminology is in widespread use? Martin Hogbin (talk) 22:34, 14 July 2009 (UTC)

It appears to be most prevalent in the robotics engineering community:

• Adaptive neural network control of robotic manipulators Shuzhi S. Ge, Tong Heng Lee, Christopher John Harris (1998)
• Fundamentals of robotic mechanical systems: theory, methods, and algorithms‎, Jorge Angeles (2003)
• Robotics and Control, R.K. Mittal and I.J. Nagrath (2003)
• Robotics and automation handbook, Thomas R. Kurfess (2004)

These are few that a quick search brought up; Brews might have some more references. Is this sufficient to establish it as a generally accepted usage of the term, at least within a significant group of researchers/engineers? --FyzixFighter (talk) 23:04, 14 July 2009 (UTC)

Yes, in robotics it is very common, and in numerical solutions of the Euler-Lagrange equations of motion. In the case of polar coordinates, three or four citations are provided in the articles where the Lagrangian approach is used and the term "generalized centrifugal force" is referred to without the "generalized" adjective. Brews ohare (talk) 23:37, 14 July 2009 (UTC)

It looks to me as though this is a rather specialized usage of the term. The article should therefore make this clear by saying something along the lines of, 'In robotics engineering it is common to use the term 'centrifugal force' ...'. Martin Hogbin (talk)

1. Swetz et al. 1997, p. 268.
2. Dugas & Maddox 1988,

• Start-Class physics articles
• Unknown-importance physics articles
• Start-Class physics articles of Unknown-importance
• Misplaced Pages requests for comment