On the Jacobi-Metric Stability Criterion

2007/05/30 by M. A. Gonzalez Leon, Leon, M. A. Gonzalez, J. L. Hernandez Pastora +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0705.4437

14 pages, no figures

arxiv created 2007/05/30 · arxiv updated 2009/12/01

Abstract

We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical approaches to the stability/instability problem are not equivalent.

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