Spacecraft Orbit Design in the Circular Restricted Three-Body Problem Using Higher-Dimensional Poincaré Maps

<p>Strategies for designing three-dimensional spacecraft trajectories in a multi-body dynamical environment are investigated using four-dimensional Poincaré maps. Unlike the planar circular restricted three-body problem, where a two-dimensional map provides a simplified view of a portion of the vast and often chaotic design space, the spatial problem requires a four-dimensional map to achieve an equivalent perspective. Such higher-dimensional maps present a visualization challenge. Furthermore, a spacecraft in the spatial problem can exhibit fundamentally more diverse and complex behavior than in the planar problem. A novel approach to four-dimensional-map-based design in the spatial circular restricted three-body problem is developed and applied to practical examples with real-world spaceflight applications involving three-dimensional trajectories in the Earth-Moon, Sun-Earth, and Uranus-Titania systems. Included in the approach is a method for representing, interpreting, and manipulating four-dimensional Poincaré maps in an interactive, three-dimensional visual environment in which the fourth dimension is displayed using color. This "space-plus-color" method expands on the "color and rotation" method of Patsis and Zachilas (used for the study of motion in a galaxy) by applying additional tools and techniques enabling design in the circular restricted three-body problem. Design is often based on maps generated by many trajectories. Image manipulation in both spatial and color dimensions is accomplished iteratively using MATLAB® and Avizo®. Four-dimensional-map-based design in the spatial circular restricted three-body problem is practical, and success is enabled by interactive tools and techniques in a visual environment. The design strategy is methodical and not restricted to any particular map formulation. Human insight is leveraged to determine reference solutions in a problem without a closed-form analytical solution. Estimates obtained through visual inspection of a map are fed into automated processes, leading to precise and/or locally-optimal solutions, including transfers to and between libration/Lagrange point orbits as well as capture, departure, and transit maneuvers near a planet or moon. Additionally, the long-term variations in instantaneous eccentricity of a high-altitude Earth orbit perturbed by lunar gravity are correlated with the shape and evolution of the surface of a deformed torus on a four-dimensional map.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Aeronautics and Astronautics

Year

2013

Author dc:creator

• Geisel, Christopher D

Contributors dc:contributor

• Kathleen C. Howell
• James M. Longuski
• William A. Crossley
• Martin J. Corless

• applied sciences
• spacecraft
• poincare maps
• three-body problem
• Aerospace Engineering

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/109

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-1106