Numerical analysis on the Hénon-Heiles model

The goal is to obtain the orbit of a star with different initial conditions.

First: Integrate the equations of motion using Runge-Kutta.

Equations of motion
Equations of motion.

Second: Since the energy equation is conserved, it can be used to calculate the error.
I don't implement this; I use an iteration limit.

An initial energy H0 is used to calculate the initial value for momentum in the x-direction.

Energy equation
Energy equation.

Third: The equations for the initial conditions. Momentum in the x-direction is calculated from the other initial conditions.

Equations for the initial conditions
Equations for the initial conditions.
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