Hénon-Heiles System

The Hénon-Heiles system is a two-degree-of-freedom Hamiltonian system, originally introduced as a model for stellar motion, with Hamiltonian

\[H(q, p) = \frac{1}{2} \big( p_1^2 + p_2^2 \big) + \frac{1}{2} \big( q_1^2 + q_2^2 \big) + q_1^2 q_2 - \frac{1}{3} q_2^3 .\]

It is a standard example of a system that transitions from regular to chaotic motion as the energy is increased.