Geodesic
Non-Smooth Geodesic Flows and Classical Mechanics
Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 209-212

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As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In fact, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q-space or the configuration space), we may define a smooth function Tg on the cotangent bundle T*M (q-p-space, or the phase space). This function is the kinetic energy of q, and locally is given by 
Marsden, J. E. Non-Smooth Geodesic Flows and Classical Mechanics. Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 209-212. doi: 10.4153/CMB-1969-023-0
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     author = {Marsden, J. E.},
     title = {Non-Smooth {Geodesic} {Flows} and {Classical} {Mechanics}},
     journal = {Canadian mathematical bulletin},
     pages = {209--212},
     year = {1969},
     volume = {12},
     number = {2},
     doi = {10.4153/CMB-1969-023-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-023-0/}
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