Lagrangian Descriptors and the Action Integral of Classical Mechanics

TL;DR

This paper integrates Lagrangian descriptors with the principle of stationary action in classical mechanics, establishing a link between Lagrangian and Hamiltonian frameworks through both deterministic and stochastic approaches.

Contribution

It introduces the use of the action as a Lagrangian descriptor, bridging Lagrangian descriptors and Hamiltonian mechanics in a unified manner.

Findings

Action can serve as a Lagrangian descriptor in various settings

Established a direct connection between Lagrangian descriptors and Hamiltonian mechanics

Illustrated the approach with benchmark examples

Abstract

In this paper we bring together the method of Lagrangian descriptors and the principle of least action, or more precisely, of stationary action, in both deterministic and stochastic settings. In particular, we show how the action can be used as a Lagrangian descriptor. This provides a direct connection between Lagrangian descriptors and Hamiltonian mechanics, and we illustrate this connection with benchmark examples.