Dynamics of a 3D Elastic String Pendulum

TL;DR

This paper develops an analytical model and a geometric numerical integrator for a 3D elastic string pendulum with a rigid body, capturing nonlinear coupling effects and preserving the Hamiltonian structure through Lie group variational integration.

Contribution

It introduces a novel geometric numerical integrator that accurately models the coupled dynamics of an elastic string and a rigid body while preserving geometric properties.

Findings

The integrator effectively captures nonlinear coupling effects.

Numerical simulations demonstrate preservation of Hamiltonian structure.

The model provides insights into complex pendulum dynamics.

Abstract

This paper presents an analytical model and a geometric numerical integrator for a rigid body connected to an elastic string, acting under a gravitational potential. Since the point where the string is attached to the rigid body is displaced from the center of mass of the rigid body, there exist nonlinear coupling effects between the string deformation and the rigid body dynamics. A geometric numerical integrator, refereed to as a Lie group variational integrator, is developed to numerically preserve the Hamiltonian structure of the presented model and its Lie group configuration manifold. These properties are illustrated by a numerical simulation.