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Non-Smooth Geodesic Flows and Classical Mechanics

Published online by Cambridge University Press:  20 November 2018

J. E. Marsden
J. E. Marsden*
Affiliation:
Princeton University
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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

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 209 - 212
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Abraham, R. and Marsden, J., Foundations of mechanics. (Benjamin, N. Y., 1967).Google Scholar
2. Marsden, J., Generalized Hamiltonian mechanics. Arch. for Rat. Mech. and Analysis 28, 5 (1968) 323–361.Google Scholar
3. Helgason, S., Differential geometry and symmetric spaces. (Academic Press, N.Y., 1962).Google Scholar