cascade.dynamics.kepler

cascade.dynamics.kepler(mu: float = 1.) → List[Tuple[heyoka.expression, heyoka.expression]]

Keplerian dynamics.

This function generates the dynamical equations of purely-Keplerian dynamics. Specifically, the returned system of differential equations will be:

\[\begin{split}\begin{cases} \frac{dx}{dt} & = v_x\\ \frac{dy}{dt} & = v_y\\ \frac{dz}{dt} & = v_z\\ \frac{dv_x}{dt} & = -\frac{\mu x}{\left( x^2+y^2+z^2 \right)^{\frac{3}{2}}}\\ \frac{dv_y}{dt} & = -\frac{\mu y}{\left( x^2+y^2+z^2 \right)^{\frac{3}{2}}}\\ \frac{dv_z}{dt} & = -\frac{\mu z}{\left( x^2+y^2+z^2 \right)^{\frac{3}{2}}} \end{cases}.\end{split}\]

Parameters:

mu (float = 1.) – The gravitational parameter.

Returns:

The system of differential equations corresponding to Keplerian dynamics.

Return type:

List[Tuple[heyoka.expression, heyoka.expression]]