Inclusion of Non-Conservative Forces in Geometric Integrators with Application to Orbit–Attitude Coupling

Abstract

In this paper, a discretization method for incorporating nonconservative forces in a class of geometric numerical integrators known as variational integrators and Galerkin variational propagators is proposed. The proposed method does not require modification of the original integration algorithm used in conservative systems. First, the damped harmonic oscillator is used as benchmark for evaluating the proposed approach. Two more complex scenarios are presented next: one considering propagations in the two-body problem with drag forces, and another dealing with long-term translational propagations about small bodies considering orbit–attitude coupled force terms where the attitude is prescribed. Numerical experiments are performed, comparing results to a nominal analytical solution when it is available, or against a highly accurate propagated reference trajectory. The results in this paper show that including the nonconservative forces in the potential energy term for the discrete equations produces a very accurate discretization. This allows one to perform accurate and fast long-term numerical propagations with structure preserving variational algorithms, in scenarios where perturbations to the system can be modeled as nonconservative forces.