I was reading the book Mathematical methods of classical mechanics by V.I.Arnold, when I came across a problem which requires us to show that the phase curves of a spherical pendulum are great circles of a sphere which we get by applying the law of conservation of energy.
I do understand that the phase space has to be 4 dimensional, and that the phase point must always lie on this S3 hypersphere.
But I am unable to prove that the phase point follows a geodesic.