Low-energy Trajectory Design (UCLA/JPL)
The summer before the my senior year at Brown University, I participated in an undergraduate research program hosted by the Institute for Pure and Applied Mathematics (IPAM) at the University of California Los Angeles (UCLA). This program, called Research in Industrial Projects for Students (RIPS), brought teams of four undergraduates to UCLA for the summer to work together on a research program proposed by industry or national laboratories.
Our project was to find a way to compute and represent the surfaces of invariant manifolds. These surfaces represent the set of minimum energy trajectories for space-craft, taking advantage of the gravitational fields of planetary, lunar or stellar bodies. Because the governing equations are nonlinear, arising from the three-body problem, there is no closed form solution, so they must be evaluated using numerical methods.
I explored the feasibility of applying of a level-set method for surface representation to the problem as an alternative to a triangular mesh grid representation. This method represents the surface of the invariant manifold as the zero level set of a function that can be evaluated numerically on a fixed Cartesian grid. One of the things I enjoyed about this project was that it allowed me to synthesize information I had learned in many of my undergraduate courses, including differential equations, linear algebra, nonlinear dynamics, numerical partial differential equations and classical mechanics. I was excited to have an opportunity to apply what I had learned in class to a real-world problem. The project required me to find ways of combining known techniques in new ways to solve a problem, which helped me see the key role creative problem solving plays in doing research .
*image from jpl.nasa.gov