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arXiv · 1508.07427

A partial reciprocal of Dirichlet Lagrange Theorem detected by Jets

G. J. Alva·M. V. P. Garcia
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Abstract

We study the stability of an equilibrium point in a conservative Hamiltonian system in the case that equilibrium is not a minimum of the potential energy and this fact is shown by a jet of this function. Thanks to a modification of a result of Krasovskii, we prove that for a large class of systems under these conditions equilibrium is unstable and there is an asymptotic trajectory to that point.

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G. J. Alva, M. V. P. Garcia. 2016-03-05. A partial reciprocal of Dirichlet Lagrange Theorem detected by Jets. https://arxiv.org/abs/1508.07427

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