Planar circular restricted three-body problem

The Hamiltonian of the planar circular restricted three-body is $$H(q,p)=\frac{p^2}{2}-\frac1{|q|}-\sqrt{1+\nu}p\cdot q^\perp-\frac{\nu}{|q-(1,0)|}+\nu q\cdot(1,0)$$ with $(q,p)\in\mathbb R^4$.

Below, you will find a plot of the trajectories in the $q$ plane, and the Poincare section in the plane $(q_1,p_1)$ with $q_2=0$, $p_2\ge \sqrt{1+\nu}q_1$. You can change the initial condition by clicking on the Poincare section.

Stop!

Build-a-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.