On the Completeness of Trajectories for Some Mechanical Systems
作者： Miguel Sánchez
DOI: 10.1007/978-1-4939-2441-7_15
关键词: Second order differential equations 、 Vector field 、 Statement (computer science) 、 Finsler manifold 、 Banach manifold 、 Algebra 、 Mathematics 、 Completeness (order theory) 、 Mathematical analysis 、 Mechanical system
摘要: The classical tools which ensure the completeness of both, vector fields and second order differential equations for mechanical systems, are revisited. Possible extensions in three directions discussed: infinite dimensional Banach (and Hilbert) manifolds, Finsler metrics pseudo-Riemannian spaces, latter including links with some relativistic spacetimes. Special emphasis is taken cleaning up known techniques, statement open questions exploration prospective frameworks.
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