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Comments about these ratings – history – watch – refresh This article covers material that is considered more important in mathematics than it is physics, hence the difference in importance ratings. Needs discussion of idea of variational principles, dynamical systems and relation to chaos and integrability, review of continuum physics (e.g. fluids, elasticity, stress). Too much focus on theory. Tompw 12:44, 5 October 2006 (UTC)

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This article covers material that is considered more important in mathematics than it is physics, hence the difference in importance ratings. Needs discussion of idea of variational principles, dynamical systems and relation to chaos and integrability, review of continuum physics (e.g. fluids, elasticity, stress). Too much focus on theory. Tompw 12:44, 5 October 2006 (UTC)

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I just exchanged 'u' and 'v' under the topic "Velocity" to represent velocities of first (by u) and second car (by v) as 'u' precedes 'v'. A minor change.

Under the topic "Frames of reference", it is stated that "Speed of light is not constant" whereas i believe that it should be "Speed of light is constant". So edited the same.

Sunil 16:29, 6 January 2006 (UTC) sunil

I changed it back to the speed of light is not constant because this article seems to cover pre-special-relativity mechanics, in which case the speed of light is not generally constant. When it comes to relativistic mechanics, the constancy of the speed of light is the difference used to derive the equations of special relativity. DAG 17:16, 19 February 2006 (UTC)

Gareth, I like some of what you've done, but I'm a bit disappointed with the resulting formatting changes. In previous versions, each concept had a separate, dilineated section with information presented in a concise, organized manner. This was useful for quick reference. Your version is more precise and reads better than earlier versions, but is less useful as a quick reference. My recommendation is to add a separate page titled "Equations of Classical Mechanics" or "Summary of Classical Mechanics", which will basically be a table of the various important equations in classical mechanics.

The page should start with definition equations for the various key parameters (eg. velocity, acceleration, force, work, kinetic energy, momentum, angular momentum, etc...). This section could then be followed by a listing of other useful equations, like x=1/2at²+v₀t+x₀. What do you think?

--Matt Stoker

Thanks for the praise. The "Equations..." page sounds like a really good idea - GWO

Personally, I would prefer defining force at least initially as, F = m*a, however, if the consensus is that F=d(m*v)/dt is more precise,

I phrased it like that for a few reasons. Its a more literal "translation" of what Newton said, you do need it for some problems (the pendulum drop sand, rocket burning fuel...) and (last and least) it fits with the concepts of relativistic mechanics (4-momenta and all that) better -- GWO

would it be preferable to first define momentum as p=m*v and then define force as F=dp/dt?

--Matt Stoker

Yes, it would be better. That way you can keep the same definition of force in relativity.

Could be. Weigh up the addition of some more notation, with the simplification of some of the equations. Would it obscure the logical flow behind F=d(m*v)/dt=m*dv/dt=m*a ? I guess the notation thing is the age-old problem of mathematical writingGWO

I find the statement that F = m a is the definition of force to be incorrect. This defines the force vector, but it does not define the force; that would be F = G M m/r^2, or F = -k x, or F = m g, etc. This is a common misconception that few professors take the time to explain. F = m a tells you that a mass is being accelerated and that it results from some force. To set up the equations of motion you must substitute the definition fo the force for F, so -k x = m a is the equation of motion.

--George Hrabovsky

Just did a major overhaul of the classical mechanics equations. Mostly I added a few equations here and there, made vector quantities bold, and changed the format to be more friendly with bold vector quantities.

Moved the request: Someone please add the equations for gravitational, electric, and magnetic forces

to this page, and responding. Gravitational may be appropriate, but electrical and magnetic force definitions belong with articles on electricity and magnetism (believe me, they're another whole ball game).

Final note: physicists divide physics in to classical and quantum mechanics. Einstein's relativity is actually lumped in with classical.

I'm not sure it's so cut and dried. I know there are quantum mechanical approximations that are based on "classical mechanics" and then if necessary relativistic corrections are tacked on.--Matt Stoker

On that topic, I came here to find out what the "opposite" of Newtonian Mechanics is so I could link it from Aerodynamics but there seem to be many different fields; now I'm confused. Could someone tell me what the field is when one can no longer assume conservation of mass and conservation of energy? moink 23:04, 26 Dec 2003 (UTC)

You can always assume conservation of energy; however in relativity conservation of mass is an approximation

I tried to address this question in "3 Limits of validity" in the article. There is not exactly an "opposite". In aerodynamics, the fundamentally different physics is mostly electromagnetism. Electromagnetism and classical mechanics were made fully consistent, only with the use of relativity, but I can't think of a way the solution to that problem affects aerodynamics. Classical electromagnetism involves fields and wave, as does classical mechanics, but when the same entity shows both wave and particle properties, as in chemistry or optical shot noise, the relevant physics is quantum mechanics. David R. Ingham 04:14, 18 March 2006 (UTC)

I've gutted the article and re-written major parts of it. It's still far from complete, but I'm structuring it after quantum mechanics, which I think has a very nice layout. Some of the removed material probably ought to be stuck back in, either here or in a separate article.

Comments are welcome. Hope I haven't ruffled any feathers :-P

Some changes, with reasons:

Removed the description of SI units. They ought to go into the respective nodes for force, mass, and so forth; in my opinion they are distractions from the presentation of the theory.
Removed most of the examples, but I want to put them back in somewhere. Some of the examples were rather disorganized, e.g. discussing the effects of gravity without having introduced gravitation. Also, Newton's law of gravitation is quite independent of the formal structure of classical mechanics, and that wasn't coming through properly.

Ultimately, I think we'll want to have links to the important sub-topics of classical mechanics: composite objects, inertial and non-inertial reference frames, oscillations, and so forth. -- CYD

Einstein long ago presented us with a radical new way to view the universe. His mathematical calculations and theories harbored destruction for the current theories of the time. The theories focused on objects such as: Planets, Galaxies, Nebulae, Gravity. Next, came Quantum Physics. These mathematical calculations and theories focused on the tiny world. Atoms, Quarks, Protons, Neutrons, Electrons...

Now, In their own right, each of the theories are correct. But, when the two theories had to be combined mathematically, they were incompatible; the math would spit out nonsense.

Recently, a new theory called string theory has surfaced. The book by Brian Greene, called The Elegant Universe, explains the theory. When positioned "between" these two theories, it can connect the two; making them compatible, and causing another revolution.

1 Rockets/physics type stuff
2 examples section
3 Small copyedit
4 Tycho ?
5 ultraviolet catastrophe
6 Sums of P
7 Do not combine Classical Mechanics with Newtonian Mechanics
- 7.1 Do not combine classical with Newtonian
8 Redirect Link?
9 Is General Relativity Part of Classical Mechanics?
10 H-bar multiplied by 2 pi ?
11 Displacement
12 About the introduction
13 merging classical and Newtonian:calling all mechanicians
14 Newtonian Kaons
15 History
16 Simple Introduction
17 Introduction
18 Vectors
19 Introduction
20 a basic problem
21 also known as Newtonian mechanics
22 Data
23 Taylor Expansion ind "The Newtonian approximation to special relativity"
24 Varying mass rocket physics
25 F'=F in two inertial reference frames "as long as m stays constant"?
26 Is Newtonian mechanics really a branch of classical mechanics ?

Rockets/physics type stuff

Hi, I need a bit o help. See, in my science class we're making rockets (out of pop bottles, but still). We can add wings, weights, etc., and the point (the part we get graded on) is to get them to go up about 20 feet (which I can do) AND to get them to go straight up and straight back down w/in 5 ft. I think of where we launched it from. Any ideas @ all on how to do this? Thanks a bundle! I don't know how often I'll be checking back here, so my e-mail is DFINEDFINE1@aol.com Thanks, much! ~~Taylor

Could someone explain how a problem involving a changing mass would sound such as decreasing rocket propellant or something like that. I'm just trying to get a feel for this since up till now I've just understood Newton's Second Law as F=ma or F=m(dv/dt). From the Newton's Laws of Motion page I got the equation F=ma+v(dm/dt) for calculating the force with a variable mass, is this right? thanks - James

examples section

It appeared that the examples section had been the result of several clashing writers, so I tried to clean it up and get a good explanation for the galilean transformation, which I think is what was trying to be explained before by the standard two cars example.

Small copyedit

In this sentence, Classical mechanics can be used to describe the motion of human-sized objects (such as tops and baseballs), many astronomical objects (such as planets and galaxies), and certain microscopic objects (such as organic molecules.) ... wouldn't it be better to replace "human-sized objects" without a more accurate, less ambiguous phrase--baseballs are NOT the size of humans. Perhaps we could say something like "objects easily perceived and manipulable on the human scale"...I'm not a great wordsmith, someone help me out 70.57.137.163 04:44, 8 Apr 2005 (UTC)

   I changed it to "macroscopic", which means just that.
   --Jeepien

Tycho ?

The lead sentence names the Classic Three post-Copernican astronomers as founders of classical mechanics. Why is this? Tycho was a superb observational astronomer, but the only thing resembling physics in his work is his abandonment of crytalline spheres for [nothing in particular, so far as I know, but that's better than spheres]. Can someone explain what I've missed here? --Dandrake 19:53, August 1, 2005 (UTC)

ultraviolet catastrophe

Isn't this more a problem of classical electromagnetism? It is the same to quantum mechanics, which includes both, but it seems to make a difference when talking about classical mechanics. --David R. Ingham

I see now that "electrodynamics" is just a redirect.

I think I will move the ultruviolet catastrophy to E&M. --David R. Ingham

Sums of P

I regard that net forces are zero when $\sum P=0$ and are also the oppesite of them. Main,brief reason might be $F=\frac{d(mv)}{dt}=0$ . :)Might be right?

--HydrogenSu 18:07, 2 February 2006 (UTC)

Do not combine Classical Mechanics with Newtonian Mechanics

Newtonian mechanics is a subfield of classical mechanics. Classical mechanics also includes La Grangian mechanics, Hamiltonian mechanics, and continuum mechanics. Newtonian mechanics was the first instance of classical mechanics, but it is not the whole of classical mechanics.

--F3meyer 20:37, 2 April 2006 (UTC)

Do not combine classical with Newtonian

I agree with F3meyer, and would only add that Einstein's theories of special and general relativity are the most obvious example of mechanics which are classical mechanics but not Newtonian. For that reason, I have taken it upon myself to remove the meger recommendation out of the article and put it into this discussion. Tom Lougheed 18:12, 7 April 2006 (UTC)

I also agree with F3, but notice that there is no general agreement that relativistic mechanncs is "classical", see below. Harald88 01:23, 20 May 2006 (UTC)

Redirect Link?

If Newtonian mechanics is different from Classical, "Newtonian Mechanics" shouldn't redirect to this page, right? Scipio Carthage (talk) 15:36, 21 March 2008 (UTC)

Is General Relativity Part of Classical Mechanics?

I am concerned that the partition of Mechanics into Classical Mechanics and Quantum Mechanics is not a generally agreed concenpt in Physics. I do agree that this kind of partition of Mechanics is good, and do not want to remove it from the article. I would just like to know what support there is for including Special and General Relativity as part of Classical Mechanics.

Since first studying Mechanics, I have regarded Special Relativity as a transitional part of physics and General Relativity as modern physics. The development of Quantum Mechanics, Special Relativity, and General Relativity all occured about the same time, about 1920. So there is no basis in chronology for treating General Relativity and Quantum Mechanics separately.

If we take a theoretic approach, Newtonian Mechanics, Lagrangian Mechanics, and Hamiltonian Mechanics have a different axiomatic basis, but they are almost dual in their theorems and to the observational facts to which they are faithful. However Special Relativity is more general in the range of facts to which it is faithful. It also requires a radical new axiom that the speed of light is the same in all inertial frames of reference. General relativity requires several new axioms not included in classical mechanics. General Relativity is faithful to observations involving speeds near the speed of light and involving mases comparable or greater than a solar mass. Newtonian Gravitational theory on the other hand is completely consistent with Newtowniam Mechanics, Lagrangian Mechanics, or Hamiltonian Mechanics. So from a theoretic approach, General Relativity is not part of Classical Mechanics.

Please discuss this topic. If there is a basis for including General Relativity in Classical Mechanics, this article will be better if that basis is referenced.

--F3meyer 23:33, 23 April 2006 (UTC)

I just wanted to start this discussion. All textbooks that I studied (such as by Alonso&Finn) have three groups:

- Classical mechanics - Relativistic mechanics - Quantum mechanics.

Thus it's incorrect to state that classical mechanics includes relativistic mechanics, as this article now does. Harald88 01:27, 20 May 2006 (UTC)

H-bar multiplied by 2 pi ?

The equation in the 'classical approximation to quantum mechanics' section includes the value ' ${2\pi\hbar}$ '. The $h b a r$ is equivalent to Plank's constant divided by $2π$ . So $h b a r$ multiplied by $2π$ is Plank's constant. So there must be a mistake somewhere - why not simply write $h$ instead of ${2\pi\hbar}$ ?

Displacement

Should position be changed to displacement because velocity is a vector not a scalar value. I thik it should, while position is correct, displacement is clearer and it implies displacement from an origin which it must be measured from.--James086 12:04, 8 August 2006 (UTC)

I need the (simple version) physics for determining the speed of wind required to topple a vehicle such as a a semi-trailor. I believe there is some ground surface friction to overcome and the density of air must be known as well as the mass of the vehicle. How do these all tie together to move or topple the truck and determine at what wind velocity would this occur?

About the introduction

The article should not start out as it does. It should explain what the topic "classical mechanics" is about. Preferably in general terms that can be understood by non-specialist readers. The advanced taxonomy can be saved for later, and should be moderated (thermodynamics is not a part of classical mechanics, for instance). However interesting, it is unlikely that someone would look up this topic in order to learn about quantum mechanics. Do we need the leading paragraphs at all? Ulcph 01:31, 1 September 2006 (UTC)

Here's what I had in mind: move the concrete description to the top, and save the following for some other time:

Classical mechanics is a branch of physics which studies the deterministic motion of objects. It includes several different branches which represent specialised forms or stages of development:

Most of the above are in some way equivalent, either exactly equivalent or equivalent under special circumstances. For example, Lagrangian mechanics is exactly equivalent to Newtonian mechanics, always, but in its simplest form, Hamiltonian mechanics is only equivalent to the prior two when no frictional or drag forces are present. In other cases, an abovementioned branch of mechanics is a convenient specialised form: Newtonian mechanics can be used to deduce statistical mechanics, and statistical mechanics directly produces, more accurately, all of the results of thermodynamics.

Classical mechanics excludes any physics which involves the uncertainty principle, so quantum mechanics is not "classical", and is sometimes called modern physics by contrast. Some sources also exclude so-called "relativistic physics" from that category. However, a number of sources do include Einstein's mechanics, which in their view represents classical mechanics in its most developed and most accurate form.

It seems to repeat things that are discussed further on anyway. Ulcph 02:28, 1 September 2006 (UTC)

Please note that an intro usually includes a basic summary! The difference in definitions is too important to omit from the intro, so I reinserted that. Apart of that, I agree that most of that text does not need to be in the intro. Harald88 09:06, 1 September 2006 (UTC)

Strangely, looking at my edit it does not appear to have been taken away, and I don't believe I did. So thanks. I only put in a space to set apart the nice hidden science-promo, in HTML-comments. Which is almost too nice to lose? Ulcph 19:55, 1 September 2006 (UTC)

I don't follow what you say...

And I now notice that I omitted by mistake:

"Quantum physics (and more specifically quantum mechanics) refers to developments since approximately 1900, starting with similarly decisive discoveries by Planck, Einstein, and Bohr".

But on second thoughts, it's better to not reinsert that there: an elaboration about quantum-mechanics doesn't really belong in the intro of an article about classical mechanics anyway. Harald88 22:59, 1 September 2006 (UTC)

Just that I did not see that I deleted that sentence - and I tend to agree that it may be rather a distaction at this place. What else I tried to say was that, I found this hidden away:

The notion of “classical“ may be somewhat confusing, insofar as this term usually refers to the era of classical antiquity in European history. While many discoveries within the mathematics of that period remain in full force today, and of the greatest use, the same cannot be said about its "science". This in no way belittles the many important developments, especially within technology, which took place in antiquity and during the Middle Ages in Europe and elsewhere.

However, the emergence of classical mechanics was a decisive stage in the development of science, in the modern sense of the term. What characterizes it, above all, is its insistence on mathematics (rather than speculation), and its reliance on experiment (rather than observation). With classical mechanics it was established how to formulate quantitative predictions in theory, and how to test them by carefully designed measurement. The emerging globally cooperative endeavor increasingly provided for much closer scrutiny and testing, both of theory and experiment. This was, and remains, a key factor in establishing certain knowledge, and in bringing it to the service of society. History shows how closely the health and wealth of a society depends on nurturing this investigative and critical approach.

Certainly gets right to the point - but maybe someone Bowdlerized it. Ulcph 22:42, 8 September 2006 (UTC)

merging classical and Newtonian:calling all mechanicians

Hello,

I see the consensus above that Newtonian mechanics should not be merged with this page. At least to me it seems that you are not basing your arguments upon the actual contents of that Wikipedia article, but on knowledge you have (above & beyond that article) which tells you that the two topics are separate and distinct.

Good.

In my opinion, the contents of that article could very easily be merged into this one. This has nothing to do with the distinctions that you have drawn here on the talk page, and everything to do with the fact that the Newtonian mechanics article offers an extremely brief & surface treatment.

I'm not arguing pro- or anti-merge; I'm asking for help. Would some of you who are knowledgeable in this area please do these two things:

either bulk up Newtonian mechanics or delete its contents and turn it into a redirect (a fate it probably doesn't deserve -- with the caveat that it might significantly overlap Newton's laws of motion)
remove the merge request from Newtonian mechanics.

The merge request has been sitting there since January, altho it was very recently turned into a "merged disputed" tag.

Could Newtonian mechanics instead be merged with Newton's laws of motion?--Ling.Nut 20:19, 18 September 2006 (UTC)

Many thanks --Ling.Nut 19:08, 18 September 2006 (UTC)

Newtonian Kaons

Here's one I have not seen before:

"Newton's own explanation avoided wave principles and resembled more the explanation for the decay of the neutral Kaons, K0 and K0 bar. That is, he supposed that the light particles were altered or excited by the glass and resonated."

It seems to "explain" something relatively simple in terms of something exceedingly complicated (probably involving the third generation and the Kobayashi-Masakawa matrix). We can do without. Ulcph 17:38, 28 September 2006 (UTC)

History

Needed a remake. Besides the beauty above, it preserves and enhances what was already there. And adds a few niceties. Ulcph 18:55, 28 September 2006 (UTC) Bold text

Simple Introduction

Some other science articles are starting to produce introductory versions of themselves to make them more accessible to the average encyclopedia reader. You can see what has been done so far at special relativity, general relativity and evolution, all of which now have special introduction articles. These are intermediate between the very simple articles on Simple Wikipedia and the regular encyclopedia articles. They serve a valuable function in producing something that is useful for getting someone up to speed so that they can then tackle the real article. Those who want even simpler explanations can drop down to Simple Wikipedia. I propose that this article as well consider an introductory version. What do you think?--Filll 22:45, 12 December 2006 (UTC)

Introduction

The wording is awful. Who wrote this? Special relativity and general relativity have nothing to do with classical mechanics. This is outrageous!!--Filll 22:45, 12 December 2006 (UTC)

Vectors

Do we really need the paragraph describing basic vector addition in the middle there? It's not really on topic. Perhaps someone should write a "vector math for physicists" article and link there. Comments? Aragh 10:45, 18 May 2007 (UTC)

Introduction

"Classical mechanics is used for..." is not a definition. How about: "In physics, classical mechanics is a theory of..."? Saying what something is used for doesn't necessarily tell what it is. - 207.61.202.185 23:46, 26 June 2007 (UTC)

a basic problem

I think there is a mistake .rational continuum mechanics is something different to classical mechanics.The later discuss point mass or rigid body motions,but the former is about construcing a mathemtical structure for mechanics of general deformable bodies.for any infomations ,look at works by Clifford Truesdell. I suggest that this page must completely change because one page for classical mechanics is enough ,but the rational mechanics does not have any pages. —The preceding unsigned comment was added by Aghamoallem (talk • contribs) 14:39, 27 June 2007.

also known as Newtonian mechanics

The phrase (also called Newtonian mechanics) has been added to the start of the lead. Actually it was originally worded "Newton physics", then "Newtonian physics", now "Newtonian mechanics". But is this worth adding at all? The alternative phrasing is already discussed at the end of the lead. —Duae Quartunciae (talk · cont) 13:57, 7 August 2007 (UTC)

Please put them all in brackets to find them directly by its links and its (correct!) different names. - Cf. e.g. Einstein effects and not Einteinian effects; especially Newton already saw light already like a wave and like a "corpuscle" (photon), ok?DeepBlueDiamond 16:51, 8 August 2007 (UTC)

OK. I have put in the correct phrasing for English, which is "Newtonian mechanics". There's nothing to wikilink, however. This is already the page for Newtonian mechanics; that link would just redirect straight back to here! Cheers —Duae Quartunciae (talk · cont) 04:49, 11 August 2007 (UTC)

Data

Notes:

1. The initial inertial velocity is a convention between the different reference frames.

2. The total tensional energy of an isolated system is equal to zero.

3. The total energy of an isolated system is equal to zero.

Sincerely,

Antonio A. Blatter —Preceding unsigned comment added by 216.244.213.251 (talk) 19:25, 11 March 2008 (UTC)

Taylor Expansion ind "The Newtonian approximation to special relativity"

There's an error in the Taylor expansion of the Lorentz Factor

$\gamma = \frac{1}{\sqrt{1-v^2/c^2}} = \left(1-\frac{v^2}{c^2}\right)^{-\frac{1}{2}} = \left(1+\left(1-\frac{v^2}{c^2}\right)^{-\frac{3}{2}} + ... \right)$

$p = \frac{m_0 v}{ \sqrt{1-v^2/c^2}} = m_0 v \left(1+\left(1-\frac{v^2}{c^2}\right)^{-\frac{3}{2}} + ... \right)$ ,

because that implies

$\gamma = \left(1 + \gamma^3 + ...\right)$ ,

and that is wrong. Also for $v < < c$ it follows $p=m_0 v \left( 1+1^{3/2} \right)= 2 m_0 v$ , which, again, is wrong. I will change that to

$p = \frac{m_0 v}{ \sqrt{1-v^2/c^2}} = m_0 v \left(1+ \frac{1}{2}\frac{v^2}{c^2} + ... \right)$

taken from

$\gamma = \left(1 + \frac{1}{2}\beta^2 + ...\right)$ ,

to be found also on the wiki page Lorentz factor. —Preceding unsigned comment added by Cholewa (talk • contribs) 14:14, 17 April 2008 (UTC)

Varying mass rocket physics

I deleted the statement about having to use the "full version" of Newton's 2nd Law for varying mass systems, where the example given was a rocket. Such a statement is false; the F=ma version of Newton's 2nd Law (which is fully correct and not a special case or deficient in any way) is completely adequate to derive the rocket equation and to form the equations of motion of a rocket. For proof, consult "Spaceflight Dynamics" by William E. Wiesel. Additionally, I work with rocket simulations every day at my job, and our simulations all use the F=ma form of Newton's 2nd Law. There is no need to modify the equation. MarcusMaximus (talk) 00:47, 19 August 2008 (UTC)

I agree. Also, in case of special relativity, the momentum is conventionally written as gamma m v and m is considered to be the constant "rest" mass (a.k.a. invariant mass, or just mass). The concept of relativistic mass (gamma times the rest mass), is not in use anymore. Count Iblis (talk) 13:15, 19 August 2008 (UTC)

Do you know why people insist on the the F=d(mv)/dt form of the equation? It seems like an unnecessary complication. Typically they also claim that this form somehow accounts for varying-mass systems. I have no idea how it does so, because when you try to use it to analyze varying mass systems you get the wrong answer. Can we propose to remove all these silly references to d(mv)/dt, and stop relegating F=ma to second-class status? In reality, people who actually use Newton's 2nd Law to model real systems know that F=ma is fully correct. MarcusMaximus (talk) 17:58, 19 August 2008 (UTC)

Perhaps for historic reasons. I think that people used to write F = dp/dt in the early days of Classical Mechanics. This can sometimes be useful. E.g. in cases where the force on an object is not due to some interaction in a field specified by a potential, but due to a large number of collisions (e.g. a spacecraft that is slowed down a bit due to collisions with dust particles). In such a case you can compute the momentum transfer to the object (using the fact that total momentum is conserved).

You can then say that dp/dt (interpreted as a coarse grained gradient) is the force exerted on the spacecraft. It is actually the coarse grained forced obtained by averaging over some time interval so that you don't see the individual collisions. Now, of course, dp/dt = m a. But you obtain dp/dt first using conservation of momentum. The acceleration and not the force will be the quantity of interest:

a = 1/m dp/dt.

Perhaps it would be interesting to include a derivation of the equation of motion for a rocket. Perhaps also a derivation of the equation of motion for a fluid (Euler's equation involving the convective derivative). Count Iblis (talk) 20:43, 19 August 2008 (UTC)

I can see how that is a valid application of the momentum form of the equation. It is only useful of the mass is constant from t₀ to t_f. As for the equations of motion of a rocket, that would be a good example of how F=d(mv)/dt doesn't account for variable mass systems, since that derivation continues to count the propellant that has left the rocket. By the way, I cleaned up your formatting a bit. Hope you don't mind. MarcusMaximus (talk) 08:08, 20 August 2008 (UTC)

F'=F in two inertial reference frames "as long as m stays constant"?

I deleted the absurd caveat that a force is the same in two different inertial reference frames as long as the mass remains constant. This is just silly; how could the mass be different in two different reference frames, or how could a changing mass cause a force to be perceived differently in two inertial reference frames? MarcusMaximus (talk) 00:51, 19 August 2008 (UTC)

Is Newtonian mechanics really a branch of classical mechanics ?

The article opens "Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof)...."

But is the mechanics of Isaac Newton expounded in his Principia really a subfield of what became 'classical mechanics', as the article claims, or are the two at least partly exclusive and conflicting ? Was classical mechanics rather a later development of mechanics that conflicted with Newton's mechanics, albeit possibly having been initiated by it ?

At least one major reason why Newton's dynamics can be construed as still a form of ancient-medieval or Aristotelian mechanics, rather than a form of classical mechanics, lies in its central notion of an inherent force of inertia that causes the perseverance of uniform motion and resists accelerated motion, as expounded in the Principia's Definition 3 of vis insita and vis inertiae. This notion was supposedly abolished in positivistic classical mechanics, which reduced forces to what Newton called 'impressed force' which only causes acceleration.

This possibility of classifying Newton's dynamics as not a form of classical mechanics was pointed out by the renowned Dutch Duhemian historian of science Jan Dijksterhuis in his classic 1957 paper The Origins of Classical Mechanics given at the University of Wisconsin Institute for the History of Science conference organised by Marshall Clagett [published in Critical Problems in the History of Science University of Wisconsin Press, 1959]. In criticism of Koyre's attempted crucial distinction between ancient-medieval and classical mechanics in the ancient-medieval concept of motion as a process which requires a force versus motion as a state which does not require any causal force allegedly in classical mechanics - an attempted distinction uncritically parroted by many academic historians of science - Dijksterhuis pointed out that Newton

"ascribes inertial motion to a Vis Inertiae, Force of Inertia, residing in the body. If the view that the fundamental difference between the ancient-medieval and classical mechanics consists in the distinction between motion-as-a-process and motion-as-a-state is to be maintained consistently, it thus appears necessary to consider Newton as not yet an exponent of classical mechanics, so that it would also become a necessity to maintain a distinction between Newtonian and classical mechanics."

In short, Newton's dynamics must be classified as a form of ancient-medieval mechanics on this analysis, a form of dynamics in accordance with the basic principle of Aristotelian dynamics that 'all motion requires a conjoined mover'. And just five years after Dijksterhuis's anti-Koyrean Duhemian observations, the Halls' 1962 publication of Newton's De Gravitatione revealed his Aristotelian theory of force and motion in its Definition 5 of force:

"Force is the causal principle of motion and rest. And it is either an external one [i.e. vis impressa ...; or it is an internal principle [i.e. vis inertiae by which existing motion or rest is conserved in a body,... " [p148 Hall & Hall 1962].

Then just over a decade after Dijksterhuis's intervention in the positiovist misinterpretaion of Newton's dynamics, Sam Westfall's 1970 Force in Newton's Physics also espoused the view that Newton's dynamics posited two different forces causing motion, namely the force of inertia that caused uniform motion and impressed force that caused accelerated motion. But the sheer irrational strength of the positivist view that uniform motion requires no cause was well illustrated in Westfall's 1993 The Life of Isaac Newton, in which Westfall quoted Newton from an early draft of his Principia's first law as saying

"...that a body, by its inherent force alone, perseveres in its state of resting or of moving uniformly in a straight line." [p167 The Life of Isaac Newton Cambridge University Press 1993]

when in an apparent severe bout of dyslexia Westfall perversely commented on this statement

"That is, inherent force ceased to be the cause of uniform motion.".

But to the contrary, in this passage Newton was obviously asserting that inherent force is the sole force causing uniform straight motion or rest to persevere. In far politer words than the late Imre Lakatos and Paul Feyerabend used to deploy about historians of science, it seems 'historians of science live in a logically parallel universe' in which their own textual evidence refutes their own conclusions.

But some 40 years later after Dijksterhuis's crucial observation in America, in his 1999 Guide to Newton's Principia (p98) the former President of the American History of Science Association and leading Newton scholar, Bernard Cohen, finally admitted that by virtue of his concept of the force of inertia in the Principia's Definition 3, Newton had not abandoned the old Aristotelian physics. Thus Cohen effectively abandoned his own longstanding positivist thesis that Newton's dynamics was 'the birth of a new physics' that overthrew Aristotelian dynamics, rather than a continuation of the old Aristotelian physics on his [Cohen's] conception of its definiing characteristic.

Perhaps one of the sharpest ways of illustrating this key difference between Newton's Newtonian dynamics and classical dynamics such as the latter is taught in A-level Physics and beyond, is to be found in their different answers to the question of how many forces operate on a body in gravitational free-fall. According to classical dynamics as I understand it is taught in A-level Physics, the answer is just one, namely the impressed force of gravity. But in Newton's dynamics it must be at least two, namely the impressed force of gravity and the inherent force of inertia that resists it. For as Newton says in his commentary on the force of inertia in the Principia's Definition 3 of the force of inertia:

"Moreover, a body exerts this force only during a change of its state, caused by another force impressed upon it, and this exercise of force is...resistance insofar as the body in order to maintain its state, strives against the impressed force,..." [p404, Cohen & Whitman 1999 Principia

However, as it transpires it is unclear that there is only one force rather than two operating in free-fall in 'classical mechanics', whatever that might be of the various different dynamical systems of such as Motte, Euler, Clairaut, d'Alembert, Lagrange, Laplace, Hamilton, Mach, Maxwell and Hertz, for example.

For example, in his historically appalling book Newton's Principia for the Common Reader that so upset Bernie Cohen, Chandrasekhar takes Maxwell's dynamical system presented in his 1877 Matter & Motion to be the canonical formulation of 'Newtonian mechanics', which he identifies with classical mechanics.

But in Maxwell's energeticist dynamics presented in that work, work itself is defined as follows:

"Work is the act of producing a change of configuration in a system in opposition to a force which resists that change." Article 72, p54.

In Article 77 Maxwell then says work done can be measured by the change in the kinetic energy produced by some force. Thus we may consider the increase in kinetic energy produced by the impressed force of gravity in gravitational free-fall, whereby work is done. It then follows immediately from Maxwell's definition of work that if work is done in free-fall, then there must also be some force of resistance to gravity in such motion, and thus at least two forces operating in free-fall. But what is the force of resistance involved here, whose existence is required by Maxwell's definition of work? Could it be Newton's force of inertia ?

Thus at least Maxwell's 'classical mechanics' must have at least two forces operating in free-fall, namely the motive force of gravity and a force of resistance to gravity, contrary to the teaching of A-level Physics that there is only one in classical mechanics. It is a matter of further research to determine what other dynamical systems of other great developers and exponents of 'classical mechanics' in addition to Maxwell, such as those listed above, also have two forces operating in free-fall, the force of gravity and some force of resistance to gravity, be it the force of inertia or whatever, in contrast with the teaching of A-level Physics that there is only one in classical mechanics.

One useful clarification of the possible difference(s) between Newton's dynamics and classical dynamics would surely be to list the Principia's 8 definition and 3 axioms, and then identify how these differ from those of classical dynamics by eliminating, revising or complementing them to produce a set of definitions and axioms that define 'classical mechanics' and highlight its comparative differentia in a clear way.

Meanwhile I flag the opening sentence to denote some justification is needed for the dubious claim that Newtonian mechanics is a subfield of classical, rather than a logically disjoint ancestor. The ultimate main issue here is that of differentiating between different versions of mechanics to understand its rational historical evolution. --Logicus (talk) 16:23, 19 September 2008 (UTC)

Aren't there several formulations of classical mechanics that continue to use the term "inertia force"? MarcusMaximus (talk) 20:10, 19 September 2008 (UTC)

Logicus: Thanks. I think you may be right, and the notion ‘inertial force’ is also to be found in such as MIT physics books on ‘Newtonian mechanics’. But of course the mere use of the term does not necessarily imply the same conception. One test of similarity/difference is whether these other formulations of classical mechanics maintain there is a force of resistance operating in free-fall. One amusing way of clarifying the issue is the comparative analysis that in free-fall there are two forces operating in Newton’s dynamics, one in classical dynamics, and none in GTR.

Re different versions of the mysterious 'classical mechanics', I offer the following chronological listing of possibly key authors and formulators in its historical evolution for consideration.

Newton, Principia 1687, 1713, 1726

Motte, A Treatise of the Mechanical Powers 1727

Euler, Mechanica 1736

Maclaurin, A Complete System of Fluxions 1742

d'Alembert, Traite de dynamique 1743

Lagrange, Mecanique analytique 1788

Laplace, Mecanique celeste 1799-1825

Poncelet Cours de Mecanique 1826

Gauss New Principles of Mechanics 1829

Poisson, Traite de Mecanique 1811/33

Hamilton, Lectures on Quaternions 1853

Kirchhoff, Lectures on mechanics 1876

Maxwell Matter and Motion 1877

Mach 1883 Mechanics

Hertz, Principles of mechanics 1894

--Logicus (talk) 14:50, 20 September 2008 (UTC)

So in Newton's formulation, how are the two forces acting on a freefalling body entered into his 2nd Law equation? My guess would be that the impressed forces and the inertial forces would be summed to zero, so

$\mathbf{F}-m\mathbf{a}=0$

Does this then become merely a semantics question? MarcusMaximus (talk) 22:39, 20 September 2008 (UTC)

Logicus comments: Not sure I understand you, but if the impressed and inertial forces were summed to net force zero, whereby F = 0, then given conservation of mass, acceleration would be zero and so it would be a uniform motion. As for your claim F – ma = 0, this is surely just an immediate logical consequence of F = ma ?

But I do not suggest Newton ever did enter the two forces into the classical mechanics equation F = ma, which Newton certainly never stated. Newton’s second law is essentially that ‘whenever a body is perturbed from rest or uniform motion by impressed forces, then the change of motion is proportional to the impressed force and acts in…..’, which proportionality is interpretable as Δv α F or Δvm α F at most. Note this law avoids any reference to inertial force, which is presumably therefore not accounted/accountable in this rule. (Also note this law does not rule out a body being perturbed from uniform motion without the action of any impressed force, such as it would be by Kepler's force of inertia or Galileo's 1590 force of impetus. The purpose of the first law is to rule out this possibility and so render acceleration/deceleration and the action of impressed force equivalent.

Of course Newton's theory of vis inertiae does become a problem when one treats inertial force as being like impressed force or a form of such and thus subject to the later classical mechanics law of motion F = ma for impressed force. (I have yet to determine when this law first emerged.)

Newton’s (Aristotelian) dynamics was conceptually very wierd and possibly incoherent, but maybe no moreso than its predecessors and successors or than mechanics has always been and still remains so: 'twas ever thus ?

As a possible matter of further interest in clarifying key hallmark differences between Newton's mechanics and classical mechanics, or what is taught as the latter in A-level Physics, in addition to there being two forces operating in gravitational free-fall in Newton's dynamics, it also analysed planetary orbital motion as the resultant of two forces, namely a centripetal impressed force of gravity and a transverse tangential inherent force of inertia {e.g. see Proposition 1 of Book 1 Principia), whereas in A-level Physics again there is only one force involved.

However, as further evidence of the tenacity of the concept of a force of inertia in ‘classical mechanics’ education, it should be noted that in her 1831 exposition of Laplace's celestial dynamics that became the standard educational exposition of 'classical dynamics' at Cambridge University in the 19th century, Mary Somerville wrote

"A planet moves in its elliptical orbit with a velocity varying every instant, in consequence of two forces, one tending to the centre of the sun, and the other in the direction of a tangent (mT,Fig. 78, Article 407) to its orbit, arising from the primitive impulse given at the time when it was launched into space." p210 Mechanism of the Heavens

This surely illustrates how the force of inertia is essentially still the force of impetus of scholastic Aristotelian dynamics such as adopted by Galileo on his 1630s dynamics, as indeed also by Newton, on Duhem's history of dynamics.

And this same dual force analysis of orbital motion was repeated in 1884 by the physicist George Gore, President of the Birmingham Scientifc Society as follows:

"...starting with the conception of two forces, one of them tending to produce continuous uniform motion in a straight line, the other tending to produce a uniformly accelerated motion towards a fixed point, [Newton] was able to show that if these dynamical assumptions were granted, Kepler's laws being consequences of them, must be universally true." [F Gore The Art of Scientific Discovery 1884, as quoted in a 1963 University of London A-level Logic paper.]

Is this just a question of semantics ?

I don’t know. Am trying to determine what empirical or other rational reasons there might be for such conceptual developments, why different people formulated all these different systems of ‘classical mechanics’ in the 18th and 19th centuries. But certainly not merely semantical for history and philosophy of science and the theory of scientific method inasmuch as the positivist thesis that Newton's and classical mechanics overthrew Aristotelian mechanics because it rejected its core thesis that all motion requires a causal force or that some forces produce uniform motion has been the cornerstone of the thesis that scientific method is revolutionary rather than gradual and reformationist. --Logicus (talk) 18:19, 22 September 2008 (UTC)

I believe you misunderstood me, based on your comment that "if the impressed and inertial forces were summed to net force zero, whereby F = 0, then given conservation of mass, acceleration would be zero and so it would be a uniform motion." The inertial force on an object as I am using the term is (minus ma). MarcusMaximus (talk) 20:29, 23 September 2008 (UTC)

Logicus: OK, sorry ! So did you mean 'the inertial force of resistance exerted by the body against the motive force of gravity acting on it = ma' ? But I cannot see any coherent dynamical analysis from this, e.g. so do we have dynamical equilibrium and thus uniform motion or not ?

But as it happens, Newton's measure of inertial force was apparently m, not ma, inasmuch as he says in Definition 3 "This force [ie vis insita is always proportional to the body and does not differ in any way from the inertia of the mass except in the manner in which it is conceived."

But note in his Definitions he defines mass (quantity of matter) as 'density x volume', and elsewhere in Principia (e.g. in Proposition 6 or 8 or thereabouts in Book 3 as I recall), he defines density as 'force of inertia per unit volume', so in effect he equates mass with force of inertia, so mass is the force of resistance m.

Thus within Aristotelian dynamics in which average speed of motion is proportional to the ratio of motive force and resistance i.e v α F/R, when the resistance is force of inertia m we have a α F/m or ma α F in Newton's development of it.

I fear understanding Newton’s dynamics is far more difficult than rocket science for those educated in classical mechanics(-: Inter alia it requires a thorough understanding of its context of 17th century Aristotelian dynamics, of which it was a development. But you can learn some of that from the section on the Middle Ages in the Wiki Celestial spheres article.

By the way, the fuller Principia quote on force of inertia than I originally provided is:

What to do about the article ? I suggest all claims about logical/conceptual relationships between Newtonian mechanics and classical mechanics should be deleted at least pro tem as far too complex to deal with, and inessential.

--Logicus (talk) 16:03, 25 September 2008 (UTC)

Is it possible that he is referring imprecisely to a 3rd law force when he says "resistance" and "strives against"? MarcusMaximus (talk) 07:15, 27 September 2008 (UTC)

Logicus comments: This is indeed a most interesting question and I am exploring the hypothesis that it was Newton's Aristotelian concept of the force of inertia that underwrote and explained Newton's third law of motion. For certainly in the case of collisions it seems the equal and opposite reaction in the form of a resistance is at least caused by the force of inertia, if not even being that very force itself. However, this becomes problematic for the crucial case of the application of the third law to attractions at a distance. But it is possibly no less problematic than Newton's extension of the third law to attractions itself. For of course Newton's attempted proof of the applicability of the third law to attractive actions at a distance as well as for collisions in the Principia's Axioms Scholium was one of the most logically farcical aspects of the Principia in respect of its proof by reductio from the risibly mistaken thesis that the first law of motion entails the impossibility of an endlessly accelerated straight motion. As Cotes pointed out to Newton, his deployment of this thesis in Book 3, Proposition 5, Corollary 1 was precisely where his attempted proof of universal mutual gravitation from 'experimental facts' (i.e. the 6 Phenomena) collapsed into circularity and was wholly vulnerable to Leibniz's public criticism that Newton had in fact not deduced it from experimental facts as he claimed. But Cotes's attempted repair of the proof of the applicability of the third law to attractions in his famous Preface to the 1713 second edition - that rather it is just contrary to experience that the whole Earth is endlessly moving straight ahead - was rather experimentally unfounded rather than absurdly invalid: he simply failed to identify what experience supposedly refuted this possibility. But the overall most important point is that all Newton's attempted celestial empirical proofs of the applicability of the third law to gravitational attraction at a distance failed because they were either refuted or unconfirmed, or else he fiddled the results.

What do you think the upshot of our discussion for the issue of deleting all claims about 'Newtonian mechanics' from the article as conceptually problematic. I note this problem is by means specific to Wikipedia, but a general problem in the field. Nevertheless it should not be repeated.--Logicus (talk) 18:23, 30 September 2008 (UTC)

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Talk:Classical mechanics.html

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Do not combine Classical Mechanics with Newtonian Mechanics

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Is Newtonian mechanics really a branch of classical mechanics ?