Analytical Study of the Primer Vector and Orbit Transfer Switching Function

• Published in: Journal of guidance, control, and dynamics control, and dynamics, 2010-01, Vol.33 (1), p.235-245
• Main Authors: Jamison, Brian Roger, Coverstone, Victoria
• Format: Article
• Language: English
• Subjects: Aerospace engineering; Algorithms; Control theory; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Optimization; Orbits; Physics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics
• ISSN: 0731-5090; 1533-3884
• DOI: 10.2514/1.41126

This work focuses on investigating the behavior of the orbit transfer switching function for the two-body problem. Recent work indicated that use of an analytical expression for the switching function could significantly reduce the computational time required to determine when to end coast arcs during trajectory optimization. This analysis of the switching function begins by showing how the primer vector and switching function in various coordinate systems are related, and two representative systems are considered for the remaining analysis. Given that multiple harmonics are manifest simultaneously in the switching function during coast arcs, some possible behaviors of such functions are considered relative to finding bounds containing the desired coast-terminating zero. It is seen that the method proposed in recent work can fail. A relatively simple improvement involving the slope of the switching function at the sampled points is used to make the method more robust and enable the production of example optimal solutions that would not have been possible with the earlier method. In terms of the two chosen systems, analytical expressions for the switching function and its derivative during coasting as well as transformation matrices that relate the systems to each other are therefore presented in Appendices . [PUBLISHER ABSTRACT]