implementations.problem_classes.HenonHeiles module¶
- class henon_heiles[source]¶
Bases:
ProblemThis class implements the second-order Hénon-Heiles system
\[\frac{d^2 x}{dt^2} = - x - 2 x y,\]\[\frac{d^2 y}{dt} = - y - x^2 + y^2\]with Hamiltonian
\[H = 0.5 \left[\left(\frac{d x}{d t}\right)^2 + \left(\frac{d y}{d t}\right)^2\right] + 0.5 \left(x^2 + y^2\right) + x^2 y - \frac{y^3}{3}.\]- dtype_f¶
alias of
acceleration
- dtype_u¶
alias of
particles
- eval_f(u, t)[source]¶
Routine to compute the right-hand side of the problem.
- Parameters:
u (dtype_u) – Current values of the particles.
t (float) – Current time of the particles is computed (not used here).
- Returns:
me – The right-hand side of the problem.
- Return type:
dtype_f