TRAJECTORY OPTIMIZATION USING ECCENTRIC LONGITUDE FORMULATION

The problem of optimal transfer using a set of nonsingular orbit eleme nts where the eccentric longitude represents the sixth state variable is extended and completed by fully considering the six-state dynamics. Because the eccentric longitude appears in the right-hand sides of th e dynamic equations, the use of this particular formulation removes th e need for solving the transcendental Kepler equation at each integrat ion step, thereby easing, to some extent, the numerical computations. Furthermore, because the eccentric longitude is being integrated direc tly, it effectively becomes an independent orbital element such that t he adjoint differential equations are derived by assuming that this lo ngitude is independent of the other elements. The variational Hamilton ian is constant throughout the transfer with the boundary conditions g iven simply in terms of the elements. An example of a general minimum- time transfer using continuous low-thrust is generated duplicating a p revious result using the mean longitude formulation to validate the ma thematical derivations.