Brent Macomber, April 3, 2015

Department of Aerospace Engineering, Texas A&M University
Enhancements of Chebyshev Picard Iteration Efficiency
for Generally Perturbed Orbits and Constrained
Dynamical Systems
Doctoral Dissertation Defense
Brent Macomber
BA, 2008 University of California, Berkeley
MS, 2011 Texas A&M University
Chair of Advisory Committee: Dr. John L. Junkins
Committee Members: Drs. Aniruddha Datta, John E. Hurtado & James D.
Turner
Friday, April 3, 2015
8:00 am – 10:00 am
H.R. Bright Building - HRBB 134
ABSTRACT
Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method
for solution of Ordinary Differential Equations (ODEs). This dissertation
presents a body of work that serves to enhance the performance and
automation of MCPI when applied to the problem of perturbed orbit
propagation. Additionally, an MCPI framework is derived that greatly
improves MCPI performance for ODE systems that intrinsically have
associated conserved quantities. Leveraging these developments, software
libraries are presented that make MCPI more accessible and automated, both
for the problem of orbit propagation, and for general ODE systems. The work
outlined in this document is the result of an effort to promote MCPI from an
algorithm of academic interest, to a broadly applicable toolset for general use
by researchers worldwide in all disciplines.
Brent Macomber is a PhD student in the Aerospace Engineering
Department, working under the supervision of Dr. John L. Junkins. He is
seeking a Guidance, Navigation, and Control job in the commercial
space industry, but will first be taking the summer off to backpack the
west coast.