Necessary conditions for singular arcs for general restricted multi-body problem
Chandeok ParkControl & Optimization Laboratories, Naval Postgraduate School, Monterrey, CA, USAI. Michael RossMechanical and Astronautical Engineering, Naval Postgraduate School, Monterrey, CA, USAQi GongApplied Mathematics and Statistics Department, University of California, Santa Cruz, CA, USAHui YanApplied Mathematics and Statistics Department, University of California, Santa Cruz, CA, USA
2010en
ABI
Abstract
We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to multiple gravitational bodies in the restricted multi-body problem. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsch condition, and an explicit formula for the singular optimal control law. Our derivations become identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer problem and show that the extremal solution is bang-singular-bang.
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