Minimum energy coplanar orbit transfer of geostationary spacecraft using time-averaged Hamiltonian

摘要

In this study, an analytical solution of the minimum-energy orbit transfer problem is derived under the assumption that the orbital motion is in the same plane throughout the transfer and that the transfer time is given. In order to solve the optimal control problem, the averaged canonical equations are derived using the time-averaged Hamiltonian. The corresponding two-point boundary-value problems are analytically integrated to form a set of nonlinear algebraic equations and the procedure to obtain the optimal trajectory and control input is presented. The analytical solutions are compared with the numerical solutions by the pseudospectral method and are found to be in good agreement.