Log-linear Dynamic Inversion for Thrusting Spacecraft on SE2(3)

We demonstrate that the error dynamics of a thrusting spacecraft are nearly group affine on the $S{E}_2(3)$ Lie group, and the nonlinearity can be bounded, or removed with the application of a dynamic inversion control law. A numerical example validates the results by showing agreement between the error predicted by the log-dynamics and the error obtained from classical integration of trajectories using Newtonian dynamics. The result clarifies how thrusting spacecraft dynamics fit within the invariant systems framework.