On the Jacobi-Metric Stability Criterion
Mathematical Physics
2007-05-31 v1 math.MP
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.
Cite
@article{arxiv.0705.4437,
title = {On the Jacobi-Metric Stability Criterion},
author = {M. A. Gonzalez Leon and J. L. Hernandez Pastora},
journal= {arXiv preprint arXiv:0705.4437},
year = {2007}
}