High-fidelity numerical simulation of complex dynamics of tethered spacecraft

Abstract

This paper presents an analytical model and a geometric numerical integrator for a tethered spacecraft model that is composed of two rigid bodies connected by an elastic tether. This high-fidelity model includes important dynamic characteristics of tethered spacecraft in orbit, namely the nonlinear coupling among tether deformations, rigid body rotational dynamics, a reeling mechanism, and orbital dynamics. A geometric numerical integrator, referred 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. This approach preserves the geometry of the configurations, and leads to accurate and efficient algorithms that have guaranteed accuracy properties that make them suitable for many dynamic simulations, especially over long simulation times. These analytical and computational models provide a reliable benchmark for testing the validity and applicability of the many simplified models in the existing literature, which have hitherto been used without careful verification that the simplifying assumptions employed are valid in physically realistic parameter regimes. We present numerical simulations which illustrate the important qualitative differences in the tethered spacecraft dynamics when the high-fidelity model is employed, as compared to models with additional simplifying assumptions.