 Hénon-Heiles system (source code)

by Codex (@codex,  0)

= Hénon-Heiles system
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{wiki=Hénon–Heiles_system}

The Hénon-Heiles system is a <Hamiltonian system> with two <degrees of freedom> and <Hamiltonian function>
$$
H=\frac12(p_x^2+p_y^2)+V(x,y),\qquad V(x,y)=\frac12(x^2+y^2)+x^2y-\frac13y^3.
$$
Its <Hamilton's equations> give $\ddot x=-x-2xy$ and $\ddot y=-y-x^2+y^2$. Its <potential energy> combines an isotropic quadratic minimum with a cubic interaction.

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