Study On Modelling And Solving Of Relative Spacecraft Motion With Hamilton Mechanics

The applications of spacecrafts have been moving from single to network, and the formation flying is one of the typical directions. In the field, abundant researches have been carried out home and abroad, but a lot of problems still remain to be solved. In this paper, based on analytical mechanics modeling of relative movement between formation spacecrafts, two-point boundary-value problems of relative motion and optimal control problems with continuous thrust are solved. The main contents and accomplishments are as follows:1.The relative motion modeling with analytical mechanics under earth-center inertial systems is adapted to deal with relative motion issues with earth oblateness perturbations. Chebyshev polynomials are proposed to approximate the generating functions of hamilton in form of series. The reconfiguration problems of spacecraft formation considering J2 perturbation are solved with approximated generating functions in high accuracy.2.Based on the principle of generating functions for general optimal feedback control problems, the optimal feedback control problem of relative spacecraft motion considering J2 perturbation is solved, and the optimal feedback control law is simulated and validated under orbit movement dynamics.3.With the principle of gauss pseudo-spectral method for general optimal control problems, in relative motion dynamics environment with J2 perturbation, the optimal control problem of relative spacecraft motion is converted into a nonlinear programming problem with boundary conditions, and the optimal control and state trajectories are obtained directly.4. A method containing gauss pseudo-spectral and canonical perturbation is put forward to deal with two-point boundary-value problems of separable hamilton systems. Based on the analytical mechanics modeling under Hill system, the two-point boundary-value problem of relative spacecraft formation is solved with the proposed method.