nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpq9g86fe4my0hhfks50t2049zlmstlfrwyd6kahh3fhg5xwc8lt3cqls5k3r (nprofile…5k3r) if it's any help, some years ago I put together a presentation on evaluating geodesics on 2D surfaces:
https://analyticphysics.com/General%20Relativity/Visualizing%20Geodesics%20on%20Surfaces.htm
It might not be detailed enough for what you're trying to do, but at least you can see how to set up the problem if you don't already know.