Low-Thrust Orbit Transfers Using Candidate Lyapunov Functions with a Mechanism for Coasting

Abstract

We consider low-thrust orbit transfers around a central body, where specified changes are sought in orbit elements except true anomaly. The desired changes in the remaining five elements can be arbitrarily large. Candidate Lyapunov functions are created based on analytic expressions for maximum rates of change of the orbit elements and the desired changes in the elements. These functions may be thought of as proximity quotients because they provide R measure of the proximity to the target orbit. The direction of thrust needed for steepest descent to the target orbit is also available analytically. The thrust is shutoff if the effectivity of the thrust at the current location on the osculating orbit is below some threshhold value. Thus, the equations of motion can be numerically integrated to obtain quickly and simply a transfer to the target orbit. A series of transfers can be easily computed to assess the trade-off between propellant mass and flight time. Preliminary comparisons to optimal solutions show that the method, while sub-optimal, performs well. *Senior Member of the Engineering Staff, Navigation and Mission Design Section, Mail-Stop 301-14OL. Member AIAA. Member AAS.

Optimization of Low-Thrust Spiral Trajectories by Collocation

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Optimization of low-thrust many-revolution transfers and Lyapunov-based guidance

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“…Dong et al [11] studied the low-thrust Lyapunov control using angular momentum and Laplace vectors. Petropoulos [12] solved low-thrust twobody orbit transfers with coasting mechanism using a candidate Lyapunov function. Later, he refined the Lyapunov control law (called Q-law by the author) [13].…”

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