Abstract:With the help of geometric mechanics, the trajectory planning of single spacecraft was discussed in this paper. The trajectory planning was divided into two procedures. Firstly, global planning algorithms are used to find a series of feasible way-points. Then, optimal controls are used to generate the motion between the way-points. Geometric mechanic focuses on the geometric character of rigid body, in which Lie group variational integrator of rigid body is derived by variational principle. The discrete mechanics and optimal control (DMOC) algorithms based on Lie group variational integrator results in a high precision optimal control of rigid body.