A Hamiltonian system whose kinetic energy is a quadratic form in the velocities is referred to as a standard, or natural, Hamiltonian system. Every Newtonian system, that is, a system of particles interacting through forces derived from a potential, i.e., of the form (1.1), belongs to this class. The trajectories of a standard system can be seen as geodesics of a suitable Riemannian manifold. This classical result is based on the variational formulation of dynamics.


Riemannian Manifold Hamiltonian System Scalar Curvature Hamiltonian Dynamics Geodesic Flow 
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© Springer Science+Business Media 2007

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