Are Hamiltonian trajectories geodesics on the cotangent bundle? Suppose we have a Hamiltonian dynamics on a phase space, whose base space is also a Riemannian manifold. I was wondering if the Hamiltonian trajectories are whether geodesics or only locally geodesics on the cotangent bundle? Thanks!
A short answer is yes, but we need some more restriction on the Hamiltonian we are choosing.  See: https://en.wikipedia.org/wiki/Geodesics_as_Hamiltonian_flows .
A short answer is yes, but we need some more restriction on the Hamiltonian we are choosing.  See: https://en.wikipedia.org/wiki/Geodesics_as_Hamiltonian_flows .