Bases: Problem
This 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
\[H = 0.5 \left[\left(\frac{d x}{d t}\right)^2 + \left(\frac{d y}{d t}\right)^2\right] + 0.5 \left(x^2 + y^2\right)
+ x^2 y - \frac{y^3}{3}.\]
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dtype_f
alias of acceleration
-
dtype_u
alias of particles
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eval_f(u, t)[source]
Routine to compute the right-hand side of the problem.
- Parameters:
-
- Returns:
me – The right-hand side of the problem.
- Return type:
dtype_f
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eval_hamiltonian(u)[source]
Routine to compute the Hamiltonian.
- Parameters:
u (dtype_u) – Current values of The particles.
- Returns:
ham – The Hamiltonian.
- Return type:
float
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u_exact(t)[source]
Routine to compute the exact/initial trajectory at time \(t\).
- Parameters:
t (float) – Time of the exact/initial trajectory.
- Returns:
me – Exact/initial position and velocity.
- Return type:
dtype_u