# Construction of numerical solution of differential equations geodesic on the sphere

I have differential equations of geodesics. I need to solve them numerically and the solution must be on a sphere.This is what the equations looks like

The geodetic on the sphere should look like this depending on the parameters

How do I numerically solve the geodesic differential equations and then plot the solution on the sphere, which would turn out as in the image above?

• Equations of geodesics on the sphere shouldn't involve symbols as $M$, $E$, $Q$, $\mu$ and $a$. What do they mean? Geodesics on simple manifolds can be found symbolically, see e.g. The time-like geodesics (orbits) in the Schwarzschild spacetime and there is no need for tackling the problem numerically. Mar 12, 2023 at 23:10
• Please post the Mathematica code about such equations. Mar 13, 2023 at 2:25
• are geodesic equations in the Kerr metric, M,E,Q,a are parameters of the black hole which lie in certain ranges they can be considered as numbers which are known. But it does not matter now, I absolutely do not understand how to solve numerically and how to write a code myself. These equations unlike the Schwarzschild equations cannot be solved analytically since this is a more complex metric. Mar 13, 2023 at 15:38