McGehee blowup for Lagrangian systems and instability of equilibria

TL;DR

This paper demonstrates that total instability is a common feature in electromagnetic Lagrangian systems, using an adapted McGehee blowup technique, and introduces new criteria for instability in various cases.

Contribution

It adapts the McGehee blowup method to electromagnetic Lagrangian systems and establishes new criteria for total instability, broadening understanding of system dynamics.

Findings

Total instability is generic in real analytic electromagnetic Lagrangian systems.

An adapted McGehee blowup technique is developed for these systems.

New criteria for total instability are proposed for different cases.

Abstract

We prove that total instability is a generic phenomenon in the real analytic class of electromagnetic Lagrangian systems under a weak magnetism hypothesis. The main object in the proof is an adaptation of the McGehee blowup for these systems. Together with this result, new criteria for total instability are introduced for both generic and non-generic cases.