Continuation from a flat to a round Earth model in the coplanar orbit transfer problem

Abstract

SUMMARYIn this article, we focus on the problem of minimization of the fuel consumption for the coplanar orbit transfer problem. This problem is usually solved numerically by a shooting method, based on the application of the Pontryagin Maximum Principle; however, the shooting method is known to be hard to initialize, and the convergence is difficult to obtain because of discontinuities of the optimal control. Several methods are known in order to overcome that problem; however, in this article, we introduce a new approach based on the following preliminary remark. When considering a 2D flat Earth model with constant gravity, the optimal control problem of passing from an initial configuration to some final configuration by minimizing the fuel consumption can be very efficiently solved, and the solution leads to a very efficient algorithm. Based on that, we propose a continuous deformation from this flat Earth model to a modified flat Earth model that is diffeomorphic to the usual round Earth model. The resulting numerical continuation process thus provides a new way to solve the problem of minimization of the fuel consumption for the coplanar orbit transfer problem. Copyright © 2011 John Wiley & Sons, Ltd.