Geodesic Equations

Geodesic equations — symbolic generation of equations of motion.

class gravica.geodesic.GeodesicEquations(equations, velocities, accelerations)

Bases: tuple

accelerations

Alias for field number 2

equations

Alias for field number 0

velocities

Alias for field number 1

gravica.geodesic.geodesic_equations(christoffel)

Generate the geodesic equations for the given spacetime.

\[\frac{d^2 x^a}{d\tau^2} + \Gamma^a_{\ bc}\,\frac{dx^b}{d\tau}\,\frac{dx^c}{d\tau} = 0\]

Returns the left-hand side for each coordinate as a GeodesicEquations namedtuple (equations, velocities, accelerations).

Velocity symbols are named d<coord>_ (e.g. dt_, dr_) and acceleration symbols dd<coord>_ (e.g. ddt_, ddr_).

Return type:

GeodesicEquations