Geometric numerical integration for 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 model includes important dynamic characteristics of tethered spacecraft in orbit, namely the nonlinear coupling between tether deformations, rotational dynamics of rigid bodies, 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. The structure-preserving properties are particularly useful for studying complex dynamics of a tethered spacecraft. These properties are illustrated by numerical simulations.

[1]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[2]  H. Troger,et al.  Modelling, Dynamics and Control of Tethered Satellite Systems , 2006 .

[3]  Claudio Bruno,et al.  satellite de-orbiting by means of electrodynamic tethers part i: general concepts and requirements , 2002 .

[4]  Wolfgang Steiner,et al.  Numerical study of large amplitude oscillations of a two-satellite continuous tether system with a varying length , 1995 .

[5]  Paul Williams.  Simple approach to orbital control using spinning electrodynamic tethers , 2006 .

[6]  Sunil K. Agrawal,et al.  Dynamic Modeling and Simulation of Satellite Tethered Systems , 2005 .

[7]  E. Hairer,et al.  Geometric Numerical Integration , 2022, Oberwolfach Reports.

[8]  Taeyoung Lee,et al.  Computational dynamics of a 3D elastic string pendulum attached to a rigid body and an inertially fixed reel mechanism , 2009, 0909.2083.

[9]  Taeyoung Lee,et al.  Dynamics of a 3D elastic string pendulum , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[10]  Luciano Iess,et al.  Linear Stability Analysis of Electrodynamic Tethers , 2005 .

[11]  D. Poelaert,et al.  On Balance and Variational Formulations of the Equation of Motion of a Body Deploying Along a Cable , 1997 .

[12]  A. Iserles,et al.  Lie-group methods , 2000, Acta Numerica.

[13]  J. Marsden,et al.  Discrete mechanics and variational integrators , 2001, Acta Numerica.

[14]  Taeyoung Lee.  Computational geometric mechanics and control of rigid bodies , 2008 .

[15]  Mario L. Cosmo,et al.  Low altitude tethered mars probe , 1990 .

[16]  Vladimir V. Beletsky,et al.  Dynamics of Space Tether Systems , 1993 .

[17]  N. McClamroch,et al.  Lie group variational integrators for the full body problem in orbital mechanics , 2007 .

[18]  M. L. Cosmo,et al.  Tethers in Space Handbook , 1997 .