- #1
Lo Scrondo
- 6
- 0
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 $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$.
I'd like to find the time averages of the two quantities. My intuition is that they arent't qualitatively different from the one-dimensional case, but I'd really welcome some help
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 $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$.
I'd like to find the time averages of the two quantities. My intuition is that they arent't qualitatively different from the one-dimensional case, but I'd really welcome some help