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Variational solutions for the heat-rate-limited aeroassisted orbital transfer problem. (English) Zbl 0858.49029

Summary: Minimum energy loss trajectories based on Pontryagin’s minimum principle are generated for the atmospheric part of an aeroassisted orbital transfer problem. At the initial time all states are given. At the final 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 inequality constraint. Numerical difficulties implied by the singularly perturbed nature of the problem are avoided by starting the integration in the interior of the trajectory at a point where the heating rate limit is active. The state constraint becomes active always in the form of a state constrained arc. Nontrivial touch points have not been observed in numerical solutions.

MSC:

49N70 Differential games and control
49N75 Pursuit and evasion games
70M20 Orbital mechanics
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