Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit

TL;DR

This paper establishes a Morse index theorem for Lagrangian systems with various boundary conditions, providing new stability criteria for brake periodic orbits through Morse index estimations.

Contribution

It introduces a Morse index theorem applicable to general boundary conditions and applies it to derive a novel stability criterion for brake periodic orbits.

Findings

Morse index theorem proven for Lagrangian systems with self-adjoint boundary conditions

New estimations on the difference of Morse indices provided

A stability criterion for brake periodic orbits derived

Abstract

In this paper, we prove Morse index theorem of Lagrangian system with any self-adjoint boundary conditions. Based on it, we give some nontrivial estimation on the difference of Morse indices. As an application, we get a new criterion for the stability problem of brake periodic orbit.