Where can I find examples for solving equations of motion in Relativity?

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Hi,

I am a new GR student and struggling a bit, to be honest. Usually in this situation I saturate myself with working through examples and eventually the penny drops, but I have not been able to find a text or any lecture notes etc. that provides examples of things like solving geodesic equations of motion given a metric ( they don't all seem responsive to the Lagrangian approach) or rewriting metrics or equations of motion in a different coordinate system etc.etc.
Can anyone help by suggesting a text?

Thanks
 
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