On the completeness of trajectories for some mechanical systems
arXiv:1303.6150
Abstract
The classical tools which ensure the completeness of vector fields and second order differential equations for mechanical systems are revisited. Possible extensions in three directions are discussed: infinite dimensional Banach and Hilbert manifolds, Finsler metrics and pseudo-Riemannian spaces, including links with some relativistic spacetimes. Special emphasis is taken in the cleaning up of known techniques, the statement of open questions and the exploration of prospective frameworks.
Five new references included, plus some discussions and minor corrections; 28 pages, 2 figures. To appear in "Geometric Mechanics: The Legacy of Jerry Marsden", Fields Institute Communications Series