Title page for ETD etd-07162001-113728

Type of Document Master's Thesis
Author Karlgaard, Christopher David
Author's Email Address karlgaard@ama-inc.com
URN etd-07162001-113728
Title Second-Order Relative Motion Equations
Degree Master of Science
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Lutze, Frederick H. Jr. Committee Chair
Cliff, Eugene M. Committee Member
Hall, Christopher D. Committee Member
  • Orbital Mechanics
  • Perturbation Methods
Date of Defense 2001-07-10
Availability unrestricted
This thesis presents an approximate solution of second order

relative motion equations. The equations of motion for a Keplerian

orbit in spherical coordinates are expanded in Taylor series form

using reference conditions consistent with that of a circular

orbit. Only terms that are linear or quadratic in state variables

are kept in the expansion. A perturbation method is employed to

obtain an approximate solution of the resulting nonlinear

differential equations. This new solution is compared with the

previously known solution of the linear case to show improvement,

and with numerical integration of the quadratic differential

equation to understand the error incurred by the approximation. In

all cases, the comparison is made by computing the difference of

the approximate state (analytical or numerical) from numerical

integration of the full nonlinear Keplerian equations of motion.

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