Dynamics of autonomous systems with external forces

TL;DR

This paper develops a geometric framework for analyzing autonomous systems under external forces, comparing variational, Lagrangian, Hamiltonian, and Poisson formulations to enhance understanding of their interrelations.

Contribution

It introduces four interconnected geometric formulations for autonomous systems with external forces, including lesser-known constructions, facilitating comprehensive analysis.

Findings

Unified geometric framework for external forces

Comparison of variational, Lagrangian, Hamiltonian, and Poisson formulations

Enhanced understanding of external forces in analytical mechanics

Abstract

We consider a geometric framework for analytical mechanics with external forces. Four versions of this framework are considered. A variational principle with boundary terms and external forces.The second and the third versions are the Lagrangian and Hamiltonian formulations,respectively. The last one is the Poisson formulation. An extensive introductory section presents some well known and some little known geometric constructions to put our formulation in the appropriate setting to make the comparison of the different formulations easier.