Passivity-preserving splitting methods for rigid body systems

TL;DR

This paper introduces passivity-preserving splitting methods for simulating rigid body systems like marine vessels, ensuring stability and energy conservation, with detailed implementation on $SO(3)$.

Contribution

It develops and proves passivity-preserving splitting methods specifically tailored for rigid body dynamics, including a reformulation on $SO(3)$ for improved numerical stability.

Findings

Methods preserve passivity in numerical simulations.

Numerical experiments confirm stability and energy behavior.

Implementation details for systems on $SO(3)$.

Abstract

A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose passivity-preserving splitting methods for the numerical solution of a class of problems which includes this system as a special case. We prove the passivity-preservation property for the splitting methods, and we investigate stability and energy behaviour in numerical experiments. Implementation is discussed in detail for a special case where the splitting gives rise to the subsequent integration of two completely integrable flows. The equations for the attitude are reformulated on $SO(3)$ using rotation matrices rather than local parametrizations with Euler angles.