Hamiltonian systems with discontinuities

TL;DR

This paper extends Hamiltonian mechanics to systems with discontinuities, introducing a novel geometric representation using coisotropic submanifolds to model rapid Hamiltonian changes.

Contribution

It proposes an original geometric framework for Hamiltonian systems with discontinuities, enhancing the understanding of rapid Hamiltonian variations.

Findings

New geometric representation of discontinuous Hamiltonian systems

Application of coisotropic submanifolds to model rapid changes

Review of different Hamiltonian formulations

Abstract

Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation of a positive homogeneous Hamiltonian system by an outer oriented coisotropic submanifold of the phase space is proposed.