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.
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}
}