The optimization of continuous constant acceleration transfer trajectories in the presence of the J_2 perturbation

摘要

The analysis of the minimum-time thrust and J_2-perturbed orbit transfer between elliptic orbits of arbitrary size, shape, and orientation, and usign continuous constant acceleration whose direction is optimized, is presented for two different formulations using nonsingular equinoctial orbit elements. A previous formulation that used the equinoctial rotating frame for the component resolution of the perturbation vector is extended to a recently developed formulation that uses the true longitude as the sixth state variable and the polar frame for the component resolution of the thrust and J_2-induced accelerations. This new analysis is much simpler because it provides the simplest form of the differential equations for the adjoints, and removes the need for solving Kepler's transcendental equation during the numerical integration of the dynamic and adjoint system of equations. Because of these simpler features, the corresponding software is also more robust resulting in improved convergence to the optimal solution of interest.