Template talk:Classical mechanics

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Hi, I just created this template for fun, but I feel it's not very accurate and exaustive. Feel free to improve it as you wish and/or leave comments on my discussion page. Thanks. Frédérick Lacasse (talk · contribs) 23:11, 21 November 2007 (UTC)

here is a comment dont bet on dead horses —Preceding unsigned comment added by 64.90.209.14 (talk) 17:24, 4 February 2008 (UTC)

[edit] Newton's notation

Newton didn't have vectors, so perhaps it would be nice to use his original notation of . On the other hand, however, Newton's second is more familiar to most as F = ma or . Perhaps the current notation is a pleasant compromise? — gogobera (talk) 00:55, 3 April 2008 (UTC)

[edit] Change the sub-legend

I propose the diagram's sub-legend 'Newton's second law of motion' be changed to 'The second law of motion of classical mechanics'.

The diagram is mistaken because its sub-legend 'Newton's second law of motion' is historically mistaken and if anything should be rather 'The second law of motion of classical mechanics'.

This is certainly not Newton's second law stated in the Principia, which was that THE change of motion [referred to in the first law] is proportional to the motive force impressed, i.e. Dmv @ F, or F --> Dmv (where 'D' = 'the absolute change', Delta, '@' = 'is proportional to', and '->' is the logical symbol for if... then...).

The misrepresentation of Newton's second law as F = ma or similar has the logical consequence that a = F/m and thus a = 0 when F = 0, whereby Newton's first law would be logically redundant just as Mach claimed it was.

But Newton's second law only deals with changes of motion produced by impressed force such as mentioned in the first law, and does not itself assert there is no change of motion without the action of impressed force as the law F = ma does, where F denotes impressed force rather than inertial force. And in fact both Galileo's 1590 Pisan impetus dynamics and Kepler's 'inertial' dynamics, both of which claimed motion would terminate without the continuing action of what Newton called 'impressed force', denied this principle.

But the logical function and historical purpose of Newton's first law is precisely to assert this principle, that there is no change of motion unless (i.e. If not) compelled by impressed force, and thus whereby Dmv <=> F, rather than just F --> Dmv. (Here <=> is the logical equivalence symbol for 'if and only if', and '-->' the symbol for 'If...then...') Thus Mach’s logical criticism was wrong by virtue of his ahistorical misinterpretation of Newton’s second law as F = ma.

Classical mechanics, whatever that might be, needs to be differentiated from Newton's mechanics.

--Logicus (talk) 18:20, 16 April 2008 (UTC)

Hi Logicus. Well, I don't know. The article on Newton's laws of motion says that the Newton second law is "The Rate of change of momentum is proportional to the resultant force producing it and takes place in the direction of that force". Isnt it the same thing that the formula on the template? (or maybe according to you, both article and template are wrong?) I do not oppose you change the sub-lengend, but honestly i'm not sure i see a true difference. Even if the formula is not as Newton stated it, it's greatly inspired by no :)?? And history remembers it as the Newton second law (improved?). Am I wrong? But your comment is interresting. Is this information on Newton laws of motion article???

Frédérick Lacasse (talk · contribs) 13:03, 17 April 2008 (UTC)

First of all, the relevant text is at wikisource, and I'll begin by saying that I disagree with Logicus on her/his proposal. Newton's second law is not stated, as such, mathematically. (Perhaps it is later in the Pricipia, I do not know.) For clarity, its statement under Axioms, or Laws of Motion reads:

The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the straight line in which that force is impressed.

(Emphasis mine, in order to make clear that this is certainly an if and only if statement. Note that Logicus has failed to quote that word in presenting his/her argument.) Since Newton used Calculus in conjunction with this law to calculate planetary orbits and such, it is not too crude to use modern calculus notation in the box, even if we choose Leibniz' d / dt notation over Newton's dot. For that matter, we use vectorial notation when Newton had none. Therefore, clearly, in modern notation, Newton's second law reads

, and I have no problem with identifying this equation (or an equivalent one) as Newton's Second Law or Newton's Second Law of Motion. Or, see Goldstein, Poole, and Safko, Classical Mechanics (3rd ed.) page 1, where is identified as Newton's second law of motion.

Regarding the other stuff you've said about Mach, historical interpretations, and other irrelevant (for the purposes here) things, perhaps this can help. Newton's second law, which can be expressed as F = ma cannot imply that "Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon" (Law 1), without presupposing the existence of inertial frames, which is what the first law, in effect, does. The fundamental disconnect between Newton and Mach, as I understand it, concerns the existence of a preferred inertial frame.

If, unlike I've read in many sources over the years, you have sources that claim Newton never equated force with a time-rate-of-change of momentum, you might be able to begin to find people willing to change their ways. However, the classical mechanics template talk is not the place for that discussion. — gogobera (talk) 20:10, 17 April 2008 (UTC)

Logicus's response to Frederick Lacasse, written before Gogobera's contribution: Thanks Frederick. Yes, BOTH the article on Newton’s laws of motion and the template are wrong, because the article mistranslates the Principia’s second law’s phrase 'mutationem motus' as ‘rate of change of momentum’, whereas it should be ‘The change of motion’, with no reference to any rate of change. It referred to an absolute change of motion as produced by an impulse, as in Cartesian vortical mechanics. May I refer you to Bernard Cohen’s ‘Guide to Newton’s Principia’ in the 1999 Cohen & Whitman Principia new translation for a good discussion of this issue, which was also touched on in the recent BBC Radio 4 ‘In Our Time’ programme on Newton’s Laws of Motion and drew the following comment from a listener published on the BBC website @ http://www.bbc.co.uk/radio4/history/inourtime/inourtime_haveyoursay.shtml

“Andrew, Newton's 3 laws

Simon Schaffer might have done well to see in this archive (dating from the programme on Popper), "if you study the original version of Newton's Second Law - not the modern F=ma - you realise that Newton regarded force as a function of time, equivalent to the modern notion of an impulse. It was change of momentum: mass *or* velocity; thus even if mass increases with increased velocity so does the force required, and Newton holds." The insertion of 'rate' in 'rate of change of motion (momentum)', giving F=ma, isn't a flaw of Newton's - it's a mistranslation of 'mutationem motus'. “

The true difference, as I have already pointed out, is that rather than Newton being illogically foolish in his axiomatisation is respect of stating a logically redundant axiom, namely Law 1, as Mach implied, because it was logically entailed by his Law 2, rather his first law states a logically independent axiom which, for example, ruled out Kepler’s theory of inertia according to which the inherent force of inertia resists and terminates all motion. For in Newton’s theory which revised the keplerian theory of inertia the force of inertia only resists accelerated motion and causes uniform straight motion like impetus did in late scholastic Aristotelian and Galilean impetus dynamics.

This is all important for understanding the logic and history of scientific discovery and such as how and why ‘classical mechanics’ emerged, the project started by Duhem that was the major research project of 20th century history and philosophy of science.. But there seems to be some considerable logical confusion and contradiction in Wikipedia articles about Newton’s dynamics and about classical mechanics and what it is and how it relates to Newtonian mechanics. For example the article on ‘Classical mechanics’ says on the one hand the two are equivalent, but on the other hand they are not equivalent because classical mechanics was created later and goes well beyond Newton’s mechanics, as in the following statements:

“There are two important alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics. They are equivalent to Newtonian mechanics, but are often more useful for solving problems.”

Versus

“While the terms classical mechanics and Newtonian mechanics are usually considered equivalent (if relativity is excluded), much of the content of classical mechanics was created in the 18th and 19th centuries and extends considerably beyond (particularly in its use of analytical mathematics) the work of Newton.”

This confusion needs sorting out, but a bigger job than I have time for. I was just trying to reduce this confusion a little, as it cropped up on the Galileo article, but I now see this diagram is pretty ubiquitous in relevant articles. Sorry just to pick on your otherwise no doubt helpful diagram.

I fear the article on Newton’s laws of motion is currently virtually wall to wall ahistorical nonsense, apparently being devoted to teaching some version of 19th century mechanics or A-level Physics rather than the history of physics.

Re your following comment

“Even if the formula is not as Newton stated it, it's greatly inspired by no :)?? And history remembers it as the Newton second law (improved?). Am I wrong?”

One problem with the first claim that Newton greatly inspired the law F = ma is that the Wikipedia classical mechanics article is currently claiming

“The proportionality between force and acceleration, am important principle in classical mechanics, was first stated by Hibat Allah Abu'l-Barakat al-Baghdaadi,[7] Ibn al-Haytham,[8] and al-Khazini.[9] “

- although I have no idea whether this is true or not.

All in all I think I should implement the proposed edit if you have no further comments or objections. But it is still unsatisfactory given it is unclear from Wikipedia what exactly classical mechanics is, whereby such as Lagrangian and Hamiltonian mechanics and even Newtonian mechanics are said to be alternative formulations of it.

The outstanding pedagogical question for your view is surely that if you claim that Newton’s second law was essentially

F = ma, then why did he think he needed to state the first law as his first axiom ? The simple answer is because it gives the equivalence between change of motion and the action of impressed force that the second law does not, because the second law is only at most Dmv α F and not Dmv = F.

--Logicus (talk) 20:34, 17 April 2008 (UTC)

See Talk:Newton's_laws_of_motion#Change_the_.27Classical_mechanics.27_diagram.27s_sub-legend_.3F for the continued discussion. — gogobera (talk) 18:51, 25 April 2008 (UTC)