- #1
Lo Scrondo
- 6
- 0
Hi everyone!
Both sources I'm currently reading (page 291 of Mathematical Methods of Classical Mechanics by Arnol'd - get it here - and page 202 of Classical Mechanics by Shapiro - here) say that, in the case of the planar harmonic oscillator, using polar or cartesian coordinate systems leads to different action-angle variables (and I'm ok with that) and different invariant tori.
I think I've understood in what sense those tori could be different (i.e. not diffeomorphic at all), but I'd be very glad to see a proof (which I found nowhere) or even an insight...
Both sources I'm currently reading (page 291 of Mathematical Methods of Classical Mechanics by Arnol'd - get it here - and page 202 of Classical Mechanics by Shapiro - here) say that, in the case of the planar harmonic oscillator, using polar or cartesian coordinate systems leads to different action-angle variables (and I'm ok with that) and different invariant tori.
I think I've understood in what sense those tori could be different (i.e. not diffeomorphic at all), but I'd be very glad to see a proof (which I found nowhere) or even an insight...