0
$\begingroup$

I am looking for a reference (or just a brief explanation) to applications of the Hamiltonian formalism to classical mechanics, e.g. to planetary motion.

In all known to me textbooks on classical mechanics explaining the Hamiltonian formalism (e.g. Landau-Lifshitz, vol. 1, or “Mathematical methods of classical mechanics” by Arnold) no applications to concrete problems of classical mechanics are given. (However this formalism plays a role later in quantum mechanics to partly motivate the Schroedinger equation.)

Improve this question
$\endgroup$
5
  • $\begingroup$ Have you checked other texts? There are 100s of textbooks on Hamiltonian methods, including books of problems with solutions, so it's difficult to answer such a broad question without some additional information. Can you provide examples from this site? There are >1700 questions tagged hamiltonian-formalism. Curiously planetary motion is best treated using Lagrangian methods: see farside.ph.utexas.edu/teaching/celestial/Celestial/… $\endgroup$
    – ZeroTheHero
    Commented Nov 19, 2022 at 19:24
  • $\begingroup$ I must admit that I did not check 100s of books. For me a good answer would be an example of a concrete problem in classical/ celestial mechanics for whose solution the Hamiltonian formalism is necessary or at least useful. I do not mean exercises from textbooks, but problems of real interest. $\endgroup$
    – user65203
    Commented Nov 19, 2022 at 19:29
  • $\begingroup$ what is a problem of real interest to you? Is this this the kind of example you want? What about this? $\endgroup$
    – ZeroTheHero
    Commented Nov 19, 2022 at 19:44
  • $\begingroup$ An example of a problem of real interest for me is explanation of the Kepler laws. (I know that they have nothing to do with Hamiltonian formalism) Another famous example is a theoretical prediction by astronomer Le Verrier of the planet Neptune. (I do not know whether Hamiltonian formalism played any role.) $\endgroup$
    – user65203
    Commented Nov 19, 2022 at 20:28
  • $\begingroup$ Perturbation theory is quite complicated as you can see from the linked text by Fitzpatrick. As to the Kepler problem, this is done via the action-angle formalism is Goldstein... $\endgroup$
    – ZeroTheHero
    Commented Nov 19, 2022 at 20:32

0

Reset to default