Recent content by Lo Scrondo

Many thanks for your insight @jambaugh! My concern was about the following fact. Let's say, in the case of the 2D SHO, we got a couple of action-angle variables, ##I_1, \omega_1## and ##I_2, \omega_2##. Now, let $$det (\frac{\partial \omega_n}{\partial I_n}) = 0$$This means that the torus...

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...

I'm studying Ergodic Theory and I think I "got" the concept, but I need an example to verify it... Let's take the simplest possible 2D classical harmonic oscillator whose kinetic energy is $$T=\frac{\dot x^2}{2}+\frac{\dot y^2}{2}$$ and potential energy is $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$...

Hi everyone! I recently came across the Lyusternik-Fet theorem concerning closed geodesics on a compact manifold. For simplicity of description, take the 2-torus, and imagine it represents the configuration space of a double pendulum. For every pair of integers m, n (where m represents the...

I've thought that this could be the motivation. Thanks for your confirm!

Many thanks for your contribution Chet, I've read many useful answers you gave here, before signing in! If I just could ask a thing...Your insight talks about entropy change in closed systems. However, doesn't the last example depict an isolated system?