henon_heiles#

diffeqzoo.ivps.henon_heiles(*, initial_values=((0.5, 0.0), (0.0, 0.1)), time_span=(0.0, 100.0), p=1.0)[source]#

Construct the Henon-Heiles problem.

The Henon-Heiles problem relates to the non-linear motion of a star around a galactic center with the motion restricted to a plane. It is a 2-dimensional, second-order differential equation and commonly solved as a 4-dimensional, first-order equation. In in its original, second-order form, it is

\[\ddot u(t) = f(u(t)),\]

with nonlinear dynamics \(f: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\).

The Henon-Heiles problem is not stiff. It is a popular benchmark problem because of its well-known Hamiltonian, which makes it a good test for symplectic integrators.

The Henon-Heiles problem is due to Henon and Heiles (1964).

BibTex for Henon and Heiles (1964)

@article{henon1964applicability,
    title={The applicability of the third integral of motion: some numerical experiments},
    author={H{\'e}non, Michel and Heiles, Carl},
    journal={The astronomical journal},
    volume={69},
    pages={73},
    year={1964}
}