Adiabatic theorem

This simulation integrates the harmonic oscillator
H = ½ p²+ ½ m ω²x²
with a frequency varying according to: ω = ω₀ + α t^β, with β ≥ 1.
It displays the full phase orbit (x,p), the last cycle starting from p = 0 and the area its area. When a cycle is completed the area is (proportional to) the action variable J. In the middle the numerical values of ∆J/J ≪ ∆ω/ω≈ ∆E/E is displayed.

The unit mass is chosen such that m = ½, the unit length such that x₀ = 1 and the unit time such that ω₀ = 1
Put the mouse pointer over an element to get information about it.

Activities

Try the options Partial and Fill.
Discuss what happens when α varies.

This is an English translation of the Basque original for a course on theoretical mechanics.
It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre. I thank Wolfgang Christian and Francisco Esquembre for their help.