Geodesics as Hamiltonian flows

Geodesics as Hamiltonian flows refer to the representation of geodesic motion (the shortest path between points on a manifold) in the language of Hamiltonian mechanics, a framework in classical mechanics that describes the evolution of dynamical systems. ### Background Concepts 1. **Geodesics**: In differential geometry, a geodesic on a manifold is a curve that represents, locally, the shortest path between points.