Quaternion Variational Integrators for Spacecraft Dynamics

Abstract

A general method for deriving variational integrators for systems with quaternion state variables is introduced. These integrators exhibit realistic energy and momentum behavior while having computational costs comparable to or less than low-order Runge-Kutta methods, making them suitable for both simulation and real-time estimation and control applications. Integrators are derived for several systems, including rigid bodies with momentum actuators and internal viscous damping. Numerical examples illustrate the performance of the integrators and an application to attitude determination using an extended Kalman filter is presented.