Dynamics of Connected Rigid Bodies in a Perfect Fluid

TL;DR

This paper develops an analytical model and a geometric numerical integrator for connected rigid bodies in a perfect fluid, capturing complex 3D fish-like locomotion and preserving Hamiltonian structure.

Contribution

It introduces a Lie group variational integrator for simulating connected rigid bodies in fluid, maintaining geometric and physical properties.

Findings

The integrator accurately models 3D fish locomotion.

Preserves Hamiltonian structure in simulations.

Demonstrates effectiveness through numerical examples.

Abstract

This paper presents an analytical model and a geometric numerical integrator for a system of rigid bodies connected by ball joints, immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space, and each joint has three rotational degrees of freedom. This model characterizes the qualitative behavior of three-dimensional fish locomotion. A geometric numerical integrator, refereed to as a Lie group variational integrator, preserves Hamiltonian structures of the presented model and its Lie group configuration manifold. These properties are illustrated by a numerical simulation for a system of three connected rigid bodies.