Geometric integration of impact during an orbital docking procedure

Simulations of orbiting bodies that experience self-impact during manuevers are known to potentially lead to numerical instability. In this paper it is demonstrated that the dynamics of an orbiting articulated body experiencing forcing and impacting can be stably simulated using variational integration. A prominent advantage of using variational integration is that conservation properties are maintained (even in the presence of external forcing) and natively can resolve impacts. Using variational integration, the configuration of the spacecraft is updated discretely to ensure that the system-subject to any applied constraints, forces, or impacts-will yield a new configuration that satisfies all conservation properties. Furthermore, variational integrators allow impacts to be easily implemented into the configuration update.