Variational integrators for interconnected Lagrange-Dirac systems

TL;DR

This paper develops a framework for discretizing interconnected Lagrange-Dirac systems that preserves geometric structures, extending previous continuous and discrete models, and demonstrates its effectiveness through simulations.

Contribution

It introduces a novel geometric structure-preserving discretization method for interconnected Lagrange-Dirac systems, building on prior continuous and discrete formulations.

Findings

Successful simulation of continuous examples demonstrating the framework's effectiveness.

Preservation of geometric structures in the discretized interconnected systems.

Extension of previous work to a discrete setting for complex interconnected models.

Abstract

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange--Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange--Dirac mechanical systems, with a view towards constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange--Dirac systems (Jacobs and Yoshimura 2014) and discrete Dirac variational integrators (Leok and Ohsawa 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura 2014.