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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)?

Rajath Radhakrishnan
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    There's e.g. the Routhian formalism. This question (v1) seems like a list question. – Qmechanic Apr 21 '15 at 14:44
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    The Koopman- von Neumann classical mechanics in Hilbert spaces; (possibly related) the $C^*$-algebraic approach to classical mechanics. – yuggib Apr 21 '15 at 14:44
  • The last bit (not quite useful) seems like an opinion-based question to me. – Kyle Kanos Apr 21 '15 at 14:46
  • @kyle how about accepted formalisms that are not common textbook or lecture material? – innisfree Apr 21 '15 at 14:50
  • @KyleKanos I'm an undergraduate student in physics and thus, I'm not aware of many theoretical methods and theories in physics. The term 'not quite useful' was included in the sense that if any other formalism was indeed very useful like the Newton's, Largrange or the Hamiltonian formalism it would be quite famous and taught to physics students. – Rajath Radhakrishnan Apr 21 '15 at 14:51
  • @Rajath: Again, a view of usefulness is going to be an opinion, no matter your level. Just because I view X as useful does not mean (a) it is and (b) that you view it as useful as well. It's just an opinion. – Kyle Kanos Apr 21 '15 at 14:58
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    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. – John Rennie Apr 21 '15 at 15:08
  • Would quaternions fit in this category? They are getting a bit more play nowadays. – Jiminion Apr 21 '15 at 15:46
  • I remember, but cannot now find, a theory by Ernst Mach that attempted to explain all potential energy in terms of kinetic energy 'hidden away' in unobservable variables, in the same way that angular motion gives rise to a centrifugal barrier for the radial motion. I will post an answer if I find it but maybe someone else will have better luck or more time than me. – Emilio Pisanty Apr 22 '15 at 13:35
  • related: https://physics.stackexchange.com/q/382596/226902 – Quillo Jun 04 '22 at 13:59

2 Answers2

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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”.

roygvib
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    See also the book "The Variational Principles of Mechanics" by Lanczos, https://books.google.fr/books/about/The_Variational_Principles_of_Mechanics.html?id=ZWoYYr8wk2IC&redir_esc=y – Quillo Jun 04 '22 at 14:13
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Kane's Method is another accepted formalism (Thomas R. Kane) which is a method for formulating equations of motion.

Jiminion
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  • Can you describe the method? There isn't a wiki page... – innisfree Apr 21 '15 at 14:50
  • www.cs.cmu.edu/~delucr/kane.doc – Jiminion Apr 21 '15 at 14:52
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    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). – Kyle Kanos Apr 21 '15 at 15:00
  • Why the downvote? Kane's method (or Kane's equations) are widely used in the fields of robotics and spacecraft modeling. It's essentially a variant of Lagrangian mechanics, but rephrased in a more computationally efficient form. – David Hammen Apr 21 '15 at 15:09
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    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? – hft Apr 21 '15 at 15:14
  • @hft Edited answer. (Sheesh.....) – Jiminion Apr 21 '15 at 15:20
  • http://grvc.us.es/publica/congresosint/documentos/Sandino_RED-UAS_Sevilla2011.pdf – Jiminion Apr 21 '15 at 15:45
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    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? – hft Apr 21 '15 at 15:50