Classical Mechanics · Hamiltonian mechanics and canonical structure
Energy ellipse and enclosed action of an oscillator
Problem
For the oscillator Hamiltonian $H=p^2/(2m)+m\omega^2q^2/2$, characterize the constant-energy curve $H=E>0$, find its intercepts, calculate its enclosed phase-space area, and evaluate the action $J=(2\pi)^{-1}\oint p\,dq$.
Hint
Find the two semiaxes by setting one phase coordinate to zero.
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