Date of Award:
Doctor of Philosophy (PhD)
Mechanical and Aerospace Engineering
This dissertation considers a deputy spacecraft constrained to remain a fixed distance from a chief spacecraft or, geometrically speaking, a deputy constrained to the surface of a sphere centered on the chief. When moving from two points on the sphere, both minimal time and minimal energy optimal control problems are investigated. Methods to speed up the computation of both the minimal time and minimal energy trajectories are presented. The underlying theory of a key system property called “Strong Observability” is further developed. The nonlinear dynamics of the spherically constrained motion are analyzed. Six equilibrium or stationary points are identified. Both periodic and chaotic motion are classified. Stabilizing control laws with corresponding regions of attraction are defined. Finally, a control law to track an arbitrary slow moving trajectory is created.
Woodford, Nathaniel T., "Spherically Constrained Relative Motion Trajectory Analysis" (2023). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 8793.
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