https://arkadiusz-jadczyk.eu/blog/2017/05/geodesics-left-invariant-metrics-matrix-lie-groups-part-1/
Geodesics of left invariant metrics on matrix Lie groups – Part 1 - Open System - Ark's blog
May 31, 2017 - An elegant derivation of geodesic equations for left invariant metrics has been given by B. Kolev in his paper "Lie groups and mechanics. An introduction"....
left invariantlie groupsopen systemgeodesicsmetrics