High-fidelity numerical simulation of complex dynamics of tethered spacecraft

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 between 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 method for validating simplifying assumptions that are typically employed in the literature, and numerical simulations are presented that demonstrate the important qualitative differences in the tethered spacecraft dynamics when high-fidelity model is employed, as compared to models with additional simplifying assumptions.