VARIATIONAL SOLUTIONS FOR THE HEAT-RATE-LIMITED AEROASSISTED ORBITAL TRANSFER PROBLEM

Minimum energy loss trajectories based on Pontryagin's minimum princip le are generated for the atmospheric part of an aeroassisted orbital t ransfer problem, At the initial time all states are given. At the fina l time the altitude, velocity, and inclination change are prescribed. Additionally, the trajectory is subject to a heating rate limit, which , in the context of optimal control, represents a first-order state in equality constraint. Numerical difficulties implied by the singularly perturbed nature of the problem are avoided by starting the integratio n in the interior of the trajectory at a point where the heating rate limit is active, The state constraint becomes active always in the for m of a state constrained are Nontrivial touch points have not been obs erved in numerical solutions.