Ian Jauslin

Coupled pendulum

The Hamiltonian of the coupled pendulum is $$H(\theta_1,\theta_2;p_1,p_2)=\frac{p_1^2}{2}+\frac{p_2^2}{2}-\omega_1^2\cos(\theta_1)-\omega_2^2\cos(\theta_2)-\epsilon\cos(\theta_1-\theta_2)$$

Below, you will find a representation of the physical system, with both pendulums swinging, a plot of the trajectories in the $\theta_1,\theta_2$ plane, and the Poincare section in the plane $(\theta_1,p_1)$ with $\theta_2=0$, $p_2\ge 0$. You can change the initial condition by clicking on the Poincare section.



Here, you can build up a phase diagram in the Poincare section. For every click, the whole Poincare section of the motion up to time $T$ will be plotted.