Minimum-Time Orbital Phasing Maneuvers

Christopher D. Hall, Victor Collazo-Perez
2003 Journal of Guidance Control and Dynamics  
The minimum-time, constant-thrust, orbital phasing maneuver is studied numerically. Non-dimensionalization reduces the problem to one where thrust magnitude and phase angle are the only parameters. Extremal solutions are obtained for the entire range of practical values of thrust magnitude and phase angle. Plots of trajectories, thrust profiles, and loci of initial costates are used to identify a near-invariance principle that leads to a variety of conclusions about this class of problems. The
more » ... ypes of thrust profiles are shown to fall into at least four types, two of which exist within the region of near-invariance. These two thrust profile types are distinguished by the time-of-flight, t f , and the transition between them takes place for a t f of approximately one-half of an orbit. The relationship between t f and the ratio of thrust to phase angle is also shown to be nearly invariant over a wide range of thrust magnitudes.
doi:10.2514/2.6921 fatcat:g66chiqrjjg4tcqld233zotvre