Small Thrust Aircraft Many Times The Space Orbit Optimization

The problem is described for the determination of optimal spacecraft trajectories in an inverse-square field using low-thrust in this paper. The differential equation of aircraft is obtained by simplification of atmospheric model, then we do non-dimensionalized the equations. The optimal transfer problem is converted into Two-Point Boundary Value Problem based on optimal control theory.On the base of all above mentioned, we study the computational methods of TPBVP. Adjoint function algorithms and direct collocation and nonlinear programming methods are applied to resolve the non-coplanar optimal orbit transfers problem. In the computational methods of TPBVP, in order to reduce some difficulties involved in solving a TPBVP via adjoint variables, we discuss a direct method in which state and control variables are indirectly parameterized, The method employs a recently developed direct optimization technique that uses a piecewise polynomial representation for the state and control variables, thus converting the optimal control problem into a nonlinear programming problem, which can be solved numerically. It makes the initial iterative variable more easy to be determined.