Talk:Centrifugal force

Choosing the redirect destination

(Copied from Talk:Centrifugal force (rotating reference frame)

I did a google on 'centrifugal force', ignoring the wikipedia I got:

• [1] - talks about rotating reference frames
• [2] rotating reference frames
• [3] rotating reference frames
• [http://hyperphysics.phy-astr.gsu.edu/HBASE/corf.html[ rotating reference frames/mach principle
• [4] doesn't exist at all
• [5] rotating reference frame
• [6] copy of columbia encyclopedia reactive centrifugal force
• [7] dunno, vague "inertia"
• [8] rotating reference frame
• [9] spam
• [10] not specified, reactive?
• [11] fictitious doesn't really exist
• [12] rotating frames of reference

Feel free to check these to make sure I've classified them correctly, and do your own googles or other kinds of searches.- (User) WolfKeeper (Talk) 00:00, 10 August 2008 (UTC)

You say "3:2 isn't a consensus at all." Could you expand on that comment? Your views were in the minority, and yet you went ahead and made your change, so I pointed out that you couldn't justify your edit based on a clear consensus of the editors. Now your answer is to tell me that "3:2 isn't a consensus at all". I know it isn't a consensus, even less so for the 2 position than for the 3 position, and yet you implemented an edit based on the 2 position. How do you justify this?

As to your web search results, you unfortunately overlooked one or two, such as

http://math.ucr.edu/home/baez/classical/inverse_square.pdf

http://www.scar.utoronto.ca/~pat/fun/NEWT3D/PDF/CORIOLIS.PDF

http://www-math.mit.edu/~djk/18_022/chapter02/section04.html

http://www.phy.umist.ac.uk/~mikeb/lecture/pc167/gravity/central.html

http://www.cbu.edu/~jholmes/P380/CentralForce.doc

http://www.myoops.org/twocw/mit/NR/rdonlyres/Mechanical-Engineering/2-141Fall-2002/1BEBB815-1441-4698-8D09-3C0E378291F3/0/spring_pendulum.pdf

This is just from about 60 seconds worth of browsing. All of these explicitly present as "centrifugal force" the term arising from the basis vectors changing in space, e.g., stationary spherical, cylindrical, polar, parabolic coordinates. I also found a cite that carefully stated centrifugal force appears only in rotating coordinates, and then proceded to derive the centrifugal force in terms of stationary polar coordinates, so one has to be careful to distinguish what people think they are doing from what they are actually doing.

Careful here. I just gave the top-hits from google, because it's the most unbiased way I know to quickly get a feel for what most people think on a subject (using multiple search engines would improve this further). Clearly there are a variety of views, but the majority are to do with rotating reference frames. Absolutely, absolutely you can come up with many references that talk about other ways of dealing with it, but rotating reference frames seems to be the most common, and this is compatible with the wikipedia's article layout. Your links above don't deal with the commonality angle at all.- (User) WolfKeeper (Talk) 15:46, 10 August 2008 (UTC)

So based on this, the redirect is currently pointed at Centrifugal force (rotating reference frame)- (User) Wolfkeeper (Talk) 16:32, 25 September 2008 (UTC)

Centripetal Force?

Why is centripetal force listed here as a branch of centrifugal force? And why is the Leibniz approach to centrifugal force[13] not listed? David Tombe (talk) 19:31, 6 May 2009 (UTC)

Centripetal force is listed as a "related concept", as are the other conceptions, because it's so closely related (like the IP editor on the talk page of the rotating frame article keeps insisting). Leibniz's isn't listed because I haven't seen a description of it that distinguishes it from the rotating reference frame concept; his equation, update to modern notation per sources, is exactly what the rotating reference frame approach comes up with, and the interpretation is also the same, at least in modern terms.

It would be good to add a section on the historical evolution of these concepts, which is where differences are likely to become apparent. We should probably start with Christiaan Huygens, who apparently coined the term. Dicklyon (talk) 20:16, 6 May 2009 (UTC)

Dick, just because you haven't seen a description of the Leibniz approach which convinces you that it is different from the rotating frames of reference approach is not a reason to suppress references to the existence of the Leibniz approach. The reference which I supplied does not mention frames of reference and I have never seen planetary orbits dealt with using rotating frames of reference. Furthermore, in planetary orbits, the Coriolis force is always in the transverse direction whereas in rotating frames of reference, the Coriolis force swings around like a signpost in the wind that has come loose at the joints. I will now undo your reverts because they were totally out of order.

As for centripetal force, it is adequately mentioned in the reactive centrifugal force section. David Tombe (talk) 07:07, 8 May 2009 (UTC)

References

FyzixFighter, it was made quite clear in the edits that the reactive centrifugal force appeared in the 1961 Nelkon & Parker, but that it was removed by the 1971 edition. There was no need for you to insert a citation tag. You should have checked how it looked before dicklyon removed most of my edits. Once again, you have arrived at a physics article for the exclusive purpose of undermining my edits. You once said to me that you would only deal in sources and not discuss physics. Now you have got sources. David Tombe (talk) 07:17, 8 May 2009 (UTC)

Technical

I'm going ahead and tagging this article as {{technical}} because I feel that it is especially important that this summary-style article remain accessible to the general reader. Those who want a highly technical in-depth analysis will go on to the branch articles. Specifically, I feel that the "Centrifugal force in planetary orbits" section needs some work to make it more readable. Please don't "dumb it down"; and I fully understand that this is not Simple WP; but it should be easily understood by the general public (think of an average high school student) with no technical background in Physics. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)

In further note, regarding my recent edit, I think I should state for the record that I am not a physicist. I am a linguist and a wikipedian. If I've made mush of any of the finer points of any of the highly technical material presented here in the process of my editing, feel free to correct me, but please do so in a way that avoids getting overly technical and encourages others to maintain civility. Thank you. Wilhelm_meis (talk) 15:12, 8 May 2009 (UTC)

Looking to this edit by FyzixFighter, I think the passages referring to Bernoulli and Lagrange need a little more clarification. Thank you for the contribution, but please remember that these articles, particularly this one, need to be easily understood by the general reader. Wilhelm_meis (talk) 02:08, 9 May 2009 (UTC)

I'll see what I can do. It's the Meli article that refers specifically to Bernoulli and Lagrange. It mentions a few others, but article goes into quite a bit of detail on Bernoulli's contribution arguing that it is in his works where "the idea that the centrifugal force is fictitious emerges unmistakably." I'll see about distill it down to a non-technical but accurate summary, but another set of eyes that has access to the article would be appreciated. In the case of Lagrange, Meli doesn't go into great detail; he just says that Lagrange's work was the main text on mechanics in the second half of the 18th century and that Lagrange explicitly stated that the centrifugal force was dependent on the rotation of a system of perpendicular axes. To say any more on Lagrange would probably need another "history of mechanics"-type reliable source - I'll keep looking. --FyzixFighter (talk) 03:29, 9 May 2009 (UTC)

I know this can be frustrating, and I really don't mean to be tendentious, but I really think the Bernoulli passage is still a bit technical. Bernoulli, in seeking to describe the motion of an object relative to an arbitrary point, showed that the magnitude of the centrifugal force depended on which arbitrary point was chosen - so far so good (the average high school student could probably grasp it), but then, and not inherently determined by the properties of the problem. I'm not sure what the properties of the problem means exactly, and I'm sure most of our readers will be left wondering as well. Sorry, but I really want to make sure we avoid jargon and highly technical explanations on this page, for the sake of those without any special background in physics. Wilhelm_meis (talk) 13:07, 9 May 2009 (UTC)

No problem. I don't mind the specific, constructive criticism. Let me think on it a bit to see if I can come up with a better wording. The idea from Meli that I'm trying to convey with properties of the problem are the inherent attributes of the bodies involved that all observers will agree on, such as mass, relative distance between bodies, charge, the elasticity of the bodies, etc. - at least that's my reading of Meli's statement. The values of these quantities don't depend on any of the observer's choices (at least in the classical sense) and so neither will the forces that result from these quantities, whereas the value for the centrifugal force does depend on the observer's choice of reference frame. Can you think of a concise but non-technical jargon-laced way to say this? --FyzixFighter (talk) 14:05, 9 May 2009 (UTC)

FyzixFighter, I'd be very surprised if Bernoulli had advocated that centrifugal force is fictitious. I have this quote from Whittaker 'A History of the Theories of Aether and Electricity; The Classical Theories (London; New York, American Institute of Physics, 1987) p.6'

ET Whittaker writes “ - - - All space, according to the young [John] Bernoulli, is permeated by a fluid Aether, containing an immense number of excessively small whirlpools. The elasticity which the Aether appears to possess, and in virtue of which it is able to transmit vibrations, is really due to the presence of these whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to dilate, and so presses against the neighbouring whirlpools - - -

It's within this context that I am particularly interested in centrifugal force. I had been aware of the Leibniz approach since 1979 but I didn't start questioning the conventional wisdom that centrifugal force is only fictitious until I tried to understand Maxwell's 1861 paper. I noticed that Maxwell was using the concept of centrifugal pressure between vortices in a similar sense to Bernoulli. I then extrapolated the Leibniz approach to the idea of two adjacent two body orbits and considered the centrifugal force term in relation to the mutual transverse speed as between objects criss-crossed between each system. It suggested that the two orbits would repel each other if the mutual transverse speeds were high enough, and that centrifugal force is indeed real.

You mentioned how Bernoulli had said that centrifugal force needs to be relative to a point origin. I would certainly agree with that, but that is not the same as saying that it needs to be associated with a rotating frame of reference. As regards the concept of rotating frames of reference, you will probably find that it began with rotating rigid bodies when they fixed a frame of reference inside those bodies to aid with the description of the motion. That'll be the Lagrange connection. I blame Coriolis (1835), for letting the concept become detached from physical reality. Gaspard-Gustave Coriolis was only interested in the physical forces associated with rotating water wheels, but he failed to see what was eventually called the Coriolis force in his first category of supplementary forces when considering the induced forces that oppose the dragging forces in a rotating frame. It seems that he didn't consider a constrained radial motion on a turntable, such as a marble running along a radial groove. Coriolis then took his 'compound centrifugal force' (Coriolis force) from the mathematical transformation equations (his second category of supplementary forces) and hence created a concept which had become totally detached from its physical context. It was a like a signpost that had become loose at the pole and allowed to blow in the wind. That is the disjointed basis for the modern science of rotating frames of reference.

I think that its time now to stand back and appraise this situation in a balanced way. You seem to be very keen to undermine all the physics edits which I make. Your record since I opened my account shows that you have only ever come to physics articles to undermine my edits. there are no exceptions to that rule. You are now trying too hard to package the Leibniz approach into the 'rotating frames' approach. If you were to fully consider the merits of the Leibniz approach, you might find that in a few days time you won't feel the need to bury it anymore.

Think about it this way. Could you fix a rotating frame of reference around two adjacent two body planetary orbits? David Tombe (talk) 11:43, 9 May 2009 (UTC)

David, please refrain from making any accusations. True or not, they serve only to perpetuate the edit warring. If you really believe someone is hounding you, go to WP:ANI. But please do not continue to post accusations on the talk pages. It doesn't help us work together or build consensus. Wilhelm_meis (talk) 12:37, 9 May 2009 (UTC)

Models or examples

I think it would help the article, it would help the general reader and it would certainly help me, if we could provide some simple models or concrete examples of each of these scenarios and phenomena to illustrate some of the more difficult concepts in a more intuitive way. Of course (and here is perhaps the real challenge) even in this pursuit we must still stick to reliable sources, lest anyone become accused of inserting their own synthesis. Anybody got any good ones in the original sources? Wilhelm_meis (talk) 12:45, 9 May 2009 (UTC)

I just added (though I forgot to login) a physical example for the reactive centrifugal force. It's taken from the Roche source. It's a little technical in terms of engineering, but it gives it a real-world, oily physical machine touch <cue Tim Allen's simian "Grunt">. If other editors think it's too technical, then we can use the old object being spun around on a string example which Roche also uses. --FyzixFighter (talk) 17:47, 9 May 2009 (UTC)

FyzixFighter, Regarding the Bernoulli reference, I don't think that you can make the deduction which you did regarding the issue of frames of reference. Bernoulli clearly points out that centrifugal force varies according to which point of reference that we choose. That is a fact of which I am well aware, and I have made my own conclusions about it. I don't intend to insert my own conclusions in the article. But you saw from my edit above that one of the Bernoulli's believed that space is filled with tiny vortices that press against each other due to centrifugal force. I have a theory that these vortices are rotating electric dipoles. It's an established fact that an electric dipole is surrouded by an inverse cube law force field. Hence if a body moves through a sea of such dipoles, it will experience an inverse cube law repulsive force relative to any arbitrarily chosen point, providing that the effect is induced by transverse motion relative to that point. That would mean that centrifugal force is built into Euclidean geometry and it would explain why centrifugal force does not show up in Cartesian coordinates. Centrifugal force hence becomes a property of absolute space and not a property of any frame of reference. That's what Newton's Bucket argument showed. But that is only my own interpretation of the situation. I don't intend to insert it. Likewise, you are entitled to deduce that Bernoulli's statement regarding centrifugal force varying according to the point of origin implies that Bernoulli was thinking in terms of frames of reference. But you are not entitled to insert that opinion into the main article.David Tombe (talk) 18:41, 9 May 2009 (UTC)

I'm not making any deduction about what Bernoulli (note this is Daniel Bernoulli, Johann Bernoulli's son) meant in his memoir. That would be original synthesis from a primary source. What I am doing is reporting what a published author says about Daniel Bernoulli's memoir in a reliable source. Your recent edit to that sentence now bears little resemblance to the statement found in that reliable source. I will make the sentence in line with the reference cited. --FyzixFighter (talk) 19:50, 9 May 2009 (UTC)

FyzixFighter, before you do so, can you not balance it out with what I wrote regarding Coriolis's role in the field of rotating frames of reference? Coriolis is much more relevant than anything that Bernoulli ever had to say on the issue of rotating frames of reference and fictitious forces. Why are you so keen to insert a quote by a man in the year 1990? It spoils the whole flow of the section. David Tombe (talk) 19:57, 9 May 2009 (UTC)

I have two sources (that I've listed) that place the paradigm shift from real force to fictitious force in the late 18th century. I've also got one more that I need to hunt down that Roche refers to: Dugas (1958) "Mechanics in the Seventeenth Century" (Neuchˆatel: Editions du Griffon). The references I've found to this source would indicate that it too places the paradigm shift in the late 18th century, but since I haven't gotten my hands on it yet, I'll wait to confirm before including it. I fail to see how this text spoils the flow of the section. The section is on the history of the centrifugal force concept, and the source is a mainstream journal on the history of science and technology. I'm keen to include it because it's from a reliable secondary source and is relevant to the topic.

I'll see if I can work in Coriolis, but to say that he is the pivot point where the paradigm shifted would require a reliable source saying as such. At most we can say that Coriolis derived all the fictitious forces in his work and gave the name compound centrifugal force to the combined outward radial components of those forces. --FyzixFighter (talk) 20:30, 9 May 2009 (UTC)

This is what I mean about sticking close to the sources and treading lightly with our models. If we move even one step away from the source it may look like we're inserting synthesis, and yet we have to make the article accessible as well. My solution to this is that we give the information as it appears in the source (i.e. either a direct quote or a close paraphrasing), and then give a parenthetical explanation in layman's terms where needed, and then give a model or concrete example that is taken directly from a source, and provide inline citations for everything. Regarding sources, I don't see a problem with using whatever sources we have available (provided that they satisfy WP:RS and WP:COI). I know it's a fine line to walk, but this group of editors is more than equal to the task, and it will help the article thrive and help us all work together. Regarding inline citations, it may sometimes be necessary to provide a note for each element of a passage (1. quote, 2. paraphrasing for clarification, 3. model) even if they came from the same source, just for the sake of clarity. Thank you all for your efforts to come together and improve this article. Wilhelm_meis (talk) 02:16, 10 May 2009 (UTC)

Experts, debates, competing, etc.

Let's don't put stuff into the article to portray the various conceptions as something involved in controversy, debates, argument among experts, etc., unless we have sources to that effect and identify the players. From all that I've read, the concepts and experts seem to co-exist peacefully, though sometimes a clarification is needed as to what technical on non-technical concept of centrifugal force is meant in a given situation. Dicklyon (talk) 16:12, 8 May 2009 (UTC)

I added some sources on the historical debates about absolute and relative motion; these can obviously stay. Brews is pretty keen on this idea, and it should expanded somewhere if it's not already; there's not much in Mach's principle. Dicklyon (talk) 17:08, 8 May 2009 (UTC)

Dick, your edits are within the basic framework for a new settlement to this long running edit war. I like the historical introduction, but there is one line which I wish to question you about. I have just left a note on Wilhelm's talk page and I mentioned that very point. I don't anticipate any further edit wars providing that the supporters of the 'rotating frames/fictitious' approach don't try to subsume the Leibniz approach.

Was there any need to mention that the planetary orbital equation (The Kepler problem) can be treated within the context of a rotating frame of reference? I did that topic in detail in 1979 at university using Williams's 'Dynamics'. I saw quite a number of methods for solving the radial second order differential equation in question. But I never saw any attempt to solve that problem using rotating frames of reference. The next year, I used Goldstein to do Lagrangian and rotating rigid body motion. As you can see, Goldstein does not use rotating frames of reference in connection with planetary orbits. Leibniz does not use rotating frames of reference either. So why the need to mention rotating frames in this context?

Let's recap what the edit war was all about. It was all about everybody but myself making sure that the Leibniz approach was kept off the page. At first I was accused of introducing original research. It took me a while to get my act together and dig up a Goldstein. But when I did, the Leibniz method was still rejected. You can look at how my first attempts to introduce the planetary orbital equation were reverted last July 2008. It indirectly led to me getting a nearly permanent block.

And now when finally the Leibniz method has been recognized due to the arrival of more sources, it seems that you are trying to subsume it into the rotating frames approach. Let's be quite clear about this. The two approaches differ in three important respects.

(1) In the rotating frames approach, centrifugal force is fictitious. In the Leibniz approach, centrifugal force is real.

(2) In the rotating frames approach, great significance is attached to the actual rotating frames themselves. In the Leibniz approach, there are no rotating frames.

(3) In the rotating frames approach, the Coriolis force swivels as like a weather cock on a pole. In the Leibniz approach, the Coriolis force is firmly fixed in the transverse direction.

So we cannot subsume the Leibniz approach into the rotating frames approach. On the centrifugal force (rotating frames of reference) page, I could see that you were all desperately trying to tangle the planetary orbital problem up with rotating frames. You were doing this as a result of momentum from the edit war. This needs to stop. Each approach now needs to be dealt with separately and in isolation, and that is the best way to ensure that there will be no return to an edit war.

So I intend to remove that sentence in the introduction which drags rotating frames of reference into the Kepler problem. There are no rotating frames of reference in the Kepler problem. David Tombe (talk) 17:13, 8 May 2009 (UTC)

I think you're fooling yourself when you say it was "all about everybody but myself making sure that the Leibniz approach was kept off the page." I introduced the Leibniz approach, and have never tried to keep it or the Goldstein approach suppressed. On the other hand, it's true that it's pretty much everyone else against you. Maybe some thoughtful self-examination is in order. Dicklyon (talk) 17:20, 8 May 2009 (UTC)

Dick, you brought it to my attention that it was the Leibniz approach and I'm grateful to you for that. I didn't realize that that approach originated with Leibniz until you showed me that link last week. But nevertheless it was that approach that I had known for 28 years when I began to try and insert it into wikipedia in early 2007. I had always known that it wasn't a Newtonian approach, and it had been my intention for years to study Newton's Principiae to try and find out exactly how Newton solved the Kepler problem. I knew that Newton got as far as the inverse square law of gravity and that he also invented calculus. On the other hand, I knew how to use Newton's law of gravity, calculus, and the inverse cube law centrifugal force to solve the Kepler problem, but I knew that it wasn't Newton's method. By producing that Leibniz reference, you have solved a long standing mystery for me. It all ties in perfectly with the notorious animosity between Newton and Leibniz. Now that I have it all clear, I can better discuss the reactive centrifugal force which I still disagree with. We're all now beginning to see how it all fits together. The initial days of the edit war in 2007 involved some editors who have long disappeared. But the thrust of it was always that they were dug into the 'rotating frames/fictitious' concept whereas I wanted a real outward centrifugal force.

On a point of curiosity, have you ever considered two × two body problems side by side in their mutual equatorial planes? If you adopt the Leibniz approach, you will be able to criss-cross a centrifugal repulsion between any pair amongst the four, providing the angular speeds are high enough. The two orbits will repel. That's how Maxwell explained magnetic repulsion. He used a sea of tiny vortices aligned solenoidally. David Tombe (talk) 20:07, 8 May 2009 (UTC)

No, I really don't know much about this stuff. Just going by what I find in books. Dicklyon (talk) 04:50, 9 May 2009 (UTC)

Physics and engineering dichotomy

Dick, I think I can live with not stating the dichotomy in the intro. But just to clarify where that came from, the Roche 2001 article is the one that casts the fictitious vs. reactive as a physics vs. engineering dichotomy. In it he states, "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." The two distinct concepts he goes on to talk about are the fictitious and reactive centrifugal forces. Since the physics/engineering dichotomy is touched on in the "reactive" section, that can be sufficient for me. Anyways, Cheers. --FyzixFighter (talk) 05:12, 9 May 2009 (UTC)

OK, thanks; no problem with it if it comes with a citation. It's funny though, as I was just discussing this with an engineering prof who assures me it's common to use the rotating-frame approach in Mech. Eng. and robotics. Dicklyon (talk) 05:39, 9 May 2009 (UTC)

Dick and FyzixFighter, It might help to calm down the edit war if everybody were to openly admit their preference. I have openly admitted that I am only in favour of the Leibniz approach. But I will not be trying to obliterate or hide the other approaches. I am not particularly interested in the 'rotating frames' approach since, in my opinion, it contains some serious errors, particularly in relation to where it has allowed the Coriolis force to swing freely like a weather cock.

It would seem to me that you are clearly committed to the 'rotating frames' approach. That's fair enough. But try not to loose sight of the contexts within which that approach is used in the textbooks. It is used mainly in relation to Coriolis problems in meteorology and missiles being fired on rotating platforms etc. In my days, it was never used in connection with the Kepler problem. You would have a hard job inserting a co-rotating frame of reference around a three body problem.

As regards the Newtonian 'reactive centrifugal force', I think that we all disagree with it and at any rate it has disappeared from the textbooks in recent years. But we can still write about it and explain its historical origins in connection with Newton's animosity towards Leibniz. The reactive approach still appears to be of interest to engineers.

As regards the issue of preferences, I have explained fully why I prefer the Leibniz approach. It is an 'all in one' approach which can explain any scenario. Start with a weak gravity hyperbolic two body problem. Then attach a string between the two bodies. The centrifugal force will pull the string taut. The induced tension in the string will then cause an inward centripetal force on top of gravity and change the orbit to circular.

Can you and FyzixFighter give me any reasons why you are so keen to promote the 'rotating frames' approach? David Tombe (talk) 12:02, 9 May 2009 (UTC)

David, thank you for asking. I came to this article with no preconceptions, not have studied how CF is treated in sources. My participation was to try to help resolve the ongoing arguments, by understanding what is in Goldstein that you kept saying others were suppressing (which was partially true), and why the topic had been split into two against the will of many editors. It was a mess. So I did what I could to move it toward an article based on sources, respecting all verifiable sourced points of view. I found that the Goldstein analysis is perfectly sensible, and not different in any significant respect from the analysis by Taylor and others that end up with the same results. I've done my best to find and cite sources, unify the treatment of the different valid points of view, etc. I found and added the Leibniz point of view and the flip that Newton had done. All good stuff, don't you agree? Dicklyon (talk) 20:41, 9 May 2009 (UTC)

Dick, I certainly think that we have all learned something new from the arguments. Originally I was only focused on getting recognition of the centrifugal force as it arose in planetary orbital theory. I only learned from you last week that that was actually Leibniz's method. I have been fascinated by that analysis for many years. I didn't do it until my second year at university and I did it over in the applied maths department. In my first year I did a classical mechanics course in the physics department and it only dealt with circular motion, and of course we were taught that centrifugal force didn't exist. Having been sold on the idea of the singular role of centripetal force in circular motion, I just couldn't figure out how to rationalize with elliptical orbits. (I was doing astronomy that year too). The next year, I did the orbital mechanics course and learned the Leibniz method. I was fascinated with the power of calculus to resolve such a difficult problem so concisely. The hyperbolic, parabolic, and elliptical solutions simply fell out of the second order differential equation. Most physics students in my time didn't do that applied maths course and I feel that they missed out on something very important. Having said that, the main thrust of that applied maths course was more on solving tricky problems centred around that theme rather than the actual theme itself, and that really was maths as opposed to physics. I remember asking my lecturer about the (Leibniz) method method and he told me that it wasn't Newton's method. I always wondered whose method it was. My specific interest in centrifugal force came many years later when I was studying Maxwell. I re-examined the Leibniz approach and realized that Maxwell was right about the fact that vortices would repel each other due to centrifugal force. We just criss-cross the centrifugal force across any permutation of pairs of particles. David Tombe (talk) 21:43, 9 May 2009 (UTC)

The connection between rotating frames and the Kepler problem?

Regarding this line in the main article,

In modern science based on Newtonian mechanics, Leibniz's centrifugal force is a subset of this conception and is a result of his viewing the motion of a planet from the standpoint of a special reference frame co-rotating with the planet.[6]

I have never seen the planetary orbital problem dealt with using a rotating frame of reference, and I have seen it done many ways using both force and energy equations. The modern science of rotating frames of reference never writes centrifugal force in its inverse cube law form, and indeed it is generally more interested in the Coriolis force. It would be impossible to insert a co-rotating frame of reference around a three body problem. So I cannot see how Leibniz's real centrifugal force can possibly be considered to be a subset of anything to do with rotating frames of reference. I don't doubt that in recent years some scientists have tried to deal with the Kepler problem using rotating frames of reference. But it definitely isn't necessary to do so and it would be a most cumbersome thing to do considering that the rate of rotation is varying. We would we bother and why do we need to have this sentence in the article? What is the exact line in the quoted reference which clarifies the reasons for this point? David Tombe (talk) 19:19, 9 May 2009 (UTC)

Some quick references that I have close at hand:

• Whiting, J.S.S. (November 1983). "Motion in a central-force field". Physics Education 18 (6): pp. 256–257
• Jeremy B. Tatum Celestial Mechanics Chapter 16 [14] (bottom of page 1, top of page 1 - the radial equation with an inverse cube centrifugal force and Tatum explicitly states that the equation describes the motion "relative to a co-rotating frame".

And from the Aiton reference:

"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." (p. 32)

"Leibniz's study of the motion along the radius vector was essentially a study of motion relative to a rotating frame of reference." (p 34)

I believe that I haven't strayed to far afield from the secondary sources and that I'm not synthesizing new conclusions from them. Do we have any reliable secondary sources that contradict this source on the question of Leibniz? You and the other editors are welcome to double-check the sources and my edits to see if I've been dishonest or remiss in reporting what they say. --FyzixFighter (talk) 20:15, 9 May 2009 (UTC)

FyzixFighter, You cannot use a co-rotating frame for the three body problem. As regards the two body problem, I didn't say that you couldn't analyze it using a rotating frame of reference. I was pointing out that it is not necessary to do so, and it was never done that way when I was studying the Kepler problem in 1979. All those references above merely tell me that some people in recent times have tried to incorporate the Leibniz approach into the modern fictitious concept. I could show references which counteract those modern opinions [15], but we shouldn't have to go down the road of a reference war. If you are serious about this topic, you will be able to judge the broader picture over a wider base of references. As it is, you need to ask yourself why you are so keen to promote the rotating frames approach. You have stated yourself that you don't form opinions and that you only copy from reliable sources. If you don't form opinions on this topic why are you so keen to edit on this page in particular and promote a particular point of view to the extent of trying to eclipse the Leibniz point of view? David Tombe (talk) 20:33, 9 May 2009 (UTC)

I fail to see how the reference you give contradicts the references I provided. Also note that the Aiton reference is from 1962 - not exactly what I would call recent times. Your reference does explain Leibniz's theory, but does not say anything about whether or not Leibniz approach can be incorporated into the modern rotating frames understanding of the centrifugal force. Interestingly, a search of your reference does yield this statement (p. 264):

"...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."

and this (p. 413, discussing eq. 11.7):

"The second term on the right-hand side is referred to as the "centrifugal force" and is due simply to the rotation of the coordinate system."

But perhaps I missed the part you're keying off of. What sentences in that text do see as contradicting the sentences from the Aiton reference?

I also fail to see where, when, or why the three-body problem entered into this discussion. I know that was one of Leibniz's biggest beefs with Newton's Principia (it didn't have a closed form solution for the 3-body problem). Does Leibniz's theory handle it, and do you have a reliable source I can look at to see how it handles it? --FyzixFighter (talk) 03:59, 10 May 2009 (UTC)

David, it's not at all clear to me what the Leibniz approach was, really; it doesn't seem to connect to dynamics as we know it. Your source says he got the equation (which is correct) from consideration of the equal areas law of Kepler among other ideas; sounds plausible. You've characterized modern sources as trying "to incorporate the Leibniz approach into the modern fictitious concept" (I presume you mean fictitious-force concept); I don't see that so much; most sources say it's consistent, if anything. I haven't seen the Aiton ref, to which the idea that the Leibniz approach is a "subset of the conception" of the rotating frame approach is attributed. I'd have to see it; I agree it sounds a bit like modern revisionism. I don't think Leibniz really treated r-double-dot as "acceleration", and probably didn't know about F=ma; Goldstein certainly did, and the only way r-double-dot can be interpreted as an acceleration is in a co-rotating frame, which he clearly did know about, and was what his "equivalent one-dimensional system" was that allowed him to go from eq 3-12 to 3-22 with the centripetal acceleration term moved over to become a centrifugal force term, just like in Taylor. I'd be surprised if Leibniz went through any analogous process in getting to the equivalent equation. Dicklyon (talk) 04:36, 10 May 2009 (UTC)

Dick, the whole thing comes down to two equations. There is a transverse equation which is essentially the law of conservation of angular momentum (Kepler's second law of planetary motion). From this equation, we can establish a constant, normally written by the symbol L. This constant L when substituted into the radial equation converts the radial equation into an equation in one variable (r) and the centrifugal force term shows up as an inverse cube law force. We then have a second order differential equation in r and it solves to yield either a hyperbola, a parabola, or an ellipse. That is the whole subject in a nutshell. Ever case scenario in this entire topic can be understood in terms of the radial equation.

What I want you to do now is to ask yourself why everybody has been so obstinate about accepting this simplistic approach to the problem. I have my own theory on that. If a person attends a course and is taught that centrifugal force does not exist, or that centrifugal force is only a fictitious force that is observed from a rotating frame of reference, you will find that they will dig into that viewpoint forever more. Recently, I checked out a local university science library. I couldn't find any physics textbooks going back earlier than the 1960's. I was told that all the old physics books had been moved away to storage in another building. The only book in that library that dealt with the Leibniz approach was the 2002 revision of Goldstein (although problem 8-23 in Taylor (2005) is the Leibniz approach without saying it). The vast majority of the books there treated centrifugal force as a fictitious force in rotating frames of reference. The more modern the books got, the more they tried to laugh off centrifugal force. One recent book published in California in the last ten years (with a picture of the Golden Gate Bridge on the cover) actually went out of its way to counteract any arguments that might be put up in favour of centrifugal force, and they did it so boldly and with such confidence. Clearly, we are in an age in which centrifugal force is not popular. It is not politically correct. My own view is that this is because the implications of it in relation to absolute motion, such as the Bucket argument do not sit comfortably with modern relativity. In relativity, frames of reference have almost taken on a physical reality in their own right.

I suspect that the instant ganging up which I encountered two years ago when I first tried to insert the Leibniz approach was because the editors involved had never heard of the Leibniz approach before and they saw that it didn't sit nicely with the rotating frames approach in the case of non-co-rotating situations. I had clearly interrupted a group that had come to a consensus and they were very keen on promoting the rotating frames approach in the special case when it is extrapolated to its ludicrous conclusions. That of course is the notion that centrifugal force even acts on a stationary object when it is observed from a rotating frame of reference, and that the Coriolis force swings into the radial direction and overrides it to cause an apparent circular motion. In my opinion, that is total nonsense and it represents the inevitable conclusion of a nonsense theory. But the editors here liked that concept too much to have it threatened by something like Leibniz's theory on planetary orbits. Hence the edit war.

You say above that you don't fully understand the Leibniz approach. I think that you do. And I think that the more it sinks in, the more you will loose any desire to promote the rotating frames appraoch or to serach around for references that try to subsume the Leibniz approach into the rotating frames approach. Such references are clearly written by men who fear the reality of centrifugal force that is implicit in the Leibniz approach. David Tombe (talk) 13:11, 10 May 2009 (UTC)

Bernoulli

FyzixFighter, regarding this line which you inserted in the main article,

In a 1746 memoir by Daniel Bernoulli, the "idea that the centrifugal force is fictitious emerges unmistakably."[5]

who exactly made that quote regarding centrifugal force being unmistakably fictitious? David Tombe (talk) 19:44, 9 May 2009 (UTC)

The author of the reliable source that is cited following that statement. --FyzixFighter (talk) 19:53, 9 May 2009 (UTC)

FyzixFighter, As I said above, that author wrote that in 1990. Bernoulli did not have any significant role to play in the development of the modern conception of rotating frames of reference. It was Coriolis. Your stuff on Bernoulli spoils the flow of the section. Bernoulli merely pointed out the interesting fact that centrifugal force depends on the point of origin. He didn't say anything about frames of reference. You cannot base an encyclopaedia on one opinion like that. David Tombe (talk) 20:01, 9 May 2009 (UTC)

It's called a WP:secondary source, which is what wikipedia is supposed to mainly rely on. Dicklyon (talk) 20:43, 9 May 2009 (UTC)

Dick, Yes I do have to accept that fact. It's a secondary source as preferred by wikipedia's rules. But I can't help thinking that more effort should be made to examine a wider range of sources to build a higher picture. It's a pity to let the opinion of one man in recent times spoil the flow of a historical evolution simply because he has had his opinion published in a journal or a book. In this case, the author makes his opinion that Bernoulli was alluding to frames of reference when it is clear that Bernoulli was alluding to the mysterious property of centrifugal force whereby it changes its value according to the chosen point of origin. It's not the same thing. That's why I would like everybody to explain more about their own personal interest in this topic, because if we all appreciate each others points of view more, then it will be easier to apply sources in a more balanced fashion. We would be able to question each other on the motive for introducing sources and we would have less responses of the kind such as 'I have no opinions, I am only reading from a source'. If they have no opinions, then why are they bothering at all? David Tombe (talk) 21:56, 9 May 2009 (UTC)

Compound Centrifugal Force

FyzixFighter, you got all that so badly wrong. Compound centrifugal force in Coriolis's paper is the Coriolis force. It takes on the mathematical form of centrifugal force but acts in any direction, and it's multiplied by 2. You tried this kind of thing out on the other page when you tried to tell us all that the centrifugal force in the radial equation was the centripetal force. You are continuing to distort the facts. I personally don't even agree with Coriolis's idea that it can act in any direction. I think that it can only act in the transverse direction. But I didn't write my opinion in. One thing is sure and that is that it is definitely not restricted to the radial direction as you have claimed. David Tombe (talk) 22:04, 9 May 2009 (UTC)

Thanks for the catch on that. I see that I misread the source. Just for everyone to see, here's the sentence I was looking at:

"The centrifugal force can therefore be decomposed into one radial centrifugal force, $m\omega ^{2}r$, and another, $-2m\omega v$, the “Coriolis force.” It is worth noting that Coriolis called the two components “forces centrifuges composées” and was interested in “his” force only in combination with the radial centrifugal force to be able to compute the total centrifugal force."

I'll adjust my previous edit and reinsert it. I do feel that the reference I'm using is superior to the one you provided since it goes into details like his focus on the waterwheel that your source did not. Neither source contains some of the details from your edit, neither do they state that Coriolis is the source of the paradigm shift that resulted in today's classical understanding of the centrifugal force and rotating reference frames. --FyzixFighter (talk) 02:10, 10 May 2009 (UTC)