On the Jacobi-Metric Stability Criterion

Details On the Jacobi-Metric Stability Criterion On the Jacobi-Metric Stability Criterion

2007-05-30

arxiv.org/abs/0705.4437v1

Physics

Mathematical Physics

14 pages, no figures

Scientific paper

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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