English

On the Lyapunov instability in Lagrangian dynamics

Dynamical Systems 2021-12-22 v3

Abstract

In the context of mechanical Lagrangian dynamics, we prove a new Lyapunov instability criterion for a non strict local minimum equilibrium point of a smooth potential where the sufficient condition for instability is the existence of a smooth solution of a certain linear PDE derived from the mechanical Lagrangian governing the dynamics. In the presence of a magnetostatic field, we also give an additional sufficient condition for the motion of a charged particle to be Lyapunov unstable.

Keywords

Cite

@article{arxiv.2108.05074,
  title  = {On the Lyapunov instability in Lagrangian dynamics},
  author = {J. M. Burgos and M. Paternain},
  journal= {arXiv preprint arXiv:2108.05074},
  year   = {2021}
}
R2 v1 2026-06-24T05:01:12.109Z