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I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are other accepted formalism of the same which are not quite useful compared to others (because otherwise if would have been famous and taught in colleges)?

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marked as duplicate by Qmechanic classical-mechanics Jun 9 '18 at 15:31

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    $\begingroup$ There's e.g. the Routhian formalism. This question (v1) seems like a list question. $\endgroup$ – Qmechanic Apr 21 '15 at 14:44
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    $\begingroup$ The Koopman- von Neumann classical mechanics in Hilbert spaces; (possibly related) the $C^*$-algebraic approach to classical mechanics. $\endgroup$ – yuggib Apr 21 '15 at 14:44
  • $\begingroup$ The last bit (not quite useful) seems like an opinion-based question to me. $\endgroup$ – Kyle Kanos Apr 21 '15 at 14:46
  • $\begingroup$ @kyle how about accepted formalisms that are not common textbook or lecture material? $\endgroup$ – innisfree Apr 21 '15 at 14:50
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    $\begingroup$ This seems a reasonable question and an interesting one. For example I had not heard of Kane's method until Jiminion mentioned it. I doubt the knowledge will revolutionise my life, but these things are always interesting to know. $\endgroup$ – John Rennie Apr 21 '15 at 15:08
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Kane's Method is another accepted formalism (Thomas R. Kane) which is a method for formulating equations of motion.

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  • $\begingroup$ Can you describe the method? There isn't a wiki page... $\endgroup$ – innisfree Apr 21 '15 at 14:50
  • $\begingroup$ www.cs.cmu.edu/~delucr/kane.doc $\endgroup$ – Jiminion Apr 21 '15 at 14:52
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    $\begingroup$ NB: LibreOffice butchers that MS Word document (which is just another reason why anyone using Word for science documents should be immediately dismissed for not using Latex/PDF). $\endgroup$ – Kyle Kanos Apr 21 '15 at 15:00
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    $\begingroup$ This isn't an answer, it's a comment. You are literally only saying that it is worth mentioning Kane's Method. The question was not about things that are worth mentioning, it is about less famous formulations of classical mechanics. What is Kane's method and why is it worth mentioning in this context? $\endgroup$ – hft Apr 21 '15 at 15:14
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    $\begingroup$ It's still a comment. Explain, don't link. E.g., I could say "Joe's Method, introduced by John J. Joe is another accepted formalism", but who is Joe and why should I care? Who accepts Joe's supposed formalism? $\endgroup$ – hft Apr 21 '15 at 15:50
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Gauss's principle of least constraint

Principles of Least Action and of Least Constraint (a review paper by E.Ramm)

If I remember correctly, this principle has been used to derive equations of motion for Gaussian isokinetic thermostat (i.e., a computational algorithm for maintaining a fixed temperature of the system). Please see, for example, Statistical Mechanics of Nonequilibrium Liquids by Denis J. Evans and Gary P. Morriss, Sec.5.2.

Excerpt from the paper by E. Ramm above (in the last page):

Gauss’s Principle is not very well known although it is mentioned as a fundamental principle in many treatises, e. g. [3, 25–27], see also [28]; correspondingly it has not been applied too often. Evans and Morriss [26] discuss in detail the application of the Principle for holonomic (constraints depend only on co-ordinates) and nonholonomic constraints (non-integrable con- straints on velocity) and conclude ”The correct application of Gauss’s principle is limited to arbitrary holonomic constraints and apparently, to nonholonomic constraint functions which are homogeneous functions of the momenta”.

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