The interplay between Dirac systems, Morse families and Interconnection

TL;DR

This paper generalizes Dirac systems using Morse families to unify various physical systems and introduces a geometric approach to interconnect Dirac systems, supported by theoretical and applied examples.

Contribution

It presents a novel geometric framework that extends Dirac systems with Morse families and describes their interconnection, applicable to multiple physical models.

Findings

Unified framework for Dirac systems and Morse families

Geometric construction of Port-Dirac systems

Demonstrated applicability through examples

Abstract

We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrained variational calculus, optimal control, Lagrangian mechanics, etc., from both the Lagrangian and the Hamiltonian viewpoint. Besides, we introduce a geometric construction of Port-Dirac systems and use it to describe the interconnection of Dirac systems. Special emphasis on theoretical and applied examples is given throughout the paper to show the applicability of the proposed framework.