Homotopy method for minimum consumption orbit transfer problem

¹ ENSEEIHT–IRIT, CNRS–UMR 5505, 2 rue Camichel, BP 7122, 31071 Toulouse Cedex 7, France; gergaud@enseeiht.fr
² Mathematics Department, 2565 Mc Carthy Mall, Honolulu HI, 96822, USA; haberkor@math.hawaii.edu

Received: 4 June 2004
Revised: 14 February 2005

Abstract

The numerical resolution of the low thrust orbital transfer problem around the Earth with the maximization of the final mass or minimization of the consumption is investigated. This problem is difficult to solve by shooting method because the optimal control is discontinuous and a homotopic method is proposed to deal with these difficulties for which convergence properties are established. For a thrust of 0.1 Newton and a final time 50% greater than the minimum one, we obtain 1786 switching times.