TWO-BODY ORBITAL BOUNDARY VALUE PROBLEMS IN REGULARIZED COORDINATES

2018 Univelt Inc. All rights reserved. Lamberts problem is widely used in preliminary design and optimization of interplanetary as well as planetocentric missions. For preliminary design, it is often necessary to obtain feasible trajectories that satisfy the mission constraints. These solutions can be used for low-fidelity trade studies and as initial guesses for high-fidelity numerical optimization. The classic Lamberts problem only allows for position and transfer time constraints. In this work, various two-body orbital boundary value problems with constraints on velocities, flight path angle, v, final radius, transfer angle, etc. are studied and their exact solutions in universal form are derived via the KS-transformation. All of the solutions are regular and completely analytic if the energy of the transfer orbit is known a priori, otherwise they reduce to solving a single transcendental equation with well-defined bounds on the roots. The formulation presented in the paper results in a single constraint in each case for solving a class of boundary value problems commonly encountered in trajectory design problems.

TWO-BODY ORBITAL BOUNDARY VALUE PROBLEMS IN REGULARIZED COORDINATES Conference Paper