  Spin-orbit coupling of planetary systems plays an important role in the
dynamics and habitability of planets. However, symplectic integrators that can
accurately simulate not only how orbit affects spin but also how spin affects
orbit have not been constructed for general systems. Thus, we develop
symplectic Lie-group integrators to simulate systems consisting gravitationally
interacting rigid bodies. A user friendly package (GRIT
\url{https://github.com/GRIT-RBSim/GRIT}) is provided and external forcings
such as tidal interactions are also included. As a demonstration, this package
is applied to Trappist-I. It shows that the differences in transit timing
variations due to spin-orbit coupling could reach a few min in ten year
measurements, and strong planetary perturbations can push Trappist-I f, g and h
out of the synchronized states.
