English

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}
}
R2 v1 2026-06-21T08:33:26.840Z