Remarks on the geometric structure of port-Hamiltonian systems

TL;DR

This paper explores the geometric structure of port-Hamiltonian systems, proposing an intrinsic, unique geometric framework based on Courant algebroids that bridges classical Hamiltonian systems and their geometric properties.

Contribution

It introduces a novel intrinsic geometric structure for port-Hamiltonian systems and establishes its uniqueness under certain conditions, linking them to Courant algebroids.

Findings

Proposes an intrinsic geometric structure for port-Hamiltonian systems.

Shows the uniqueness of this geometric structure if it exists.

Connects port-Hamiltonian systems to Courant algebroid morphisms.

Abstract

We study the geometric structure of port-Hamiltonian systems. Starting with the intuitive understanding that port-Hamiltonian systems are "in between" certain closed Hamiltonian systems, the geometric structure of port-Hamiltonian systems must be "in between" the geometric structures of the latter systems. These are Courant algebroids; and hence the geometric structures should be related by Courant algebroid morphisms. Using this idea, we propose a definition of an intrinsic geometric structure and show that it is unique, if it exists.