Date of Award

12-1992

Document Type

Thesis

Degree Name

Master of Science

Department

Department of Aeronautics and Astronautics

First Advisor

William E. Wiesel, PhD

Abstract

Classical Floquet theory is examined in order to generate a canonical transformation to modal variables for periodic system This transformation is considered canonical if the periodic matrix of eigenvectors is symplectic at the initial time. Approaches for symplectic normalization of the eigenvectors had to be examined for each of the different Poincare eigenvalue cases. Particular attention was required in the degenerate case, which depended on the solution of a generalized eigenvector. Transformation techniques to ensure real modal variables and real periodic eigenvectors were also needed. Periodic trajectories in the restricted three-body case were then evaluated using the canonical Floquet solution. The system used for analyses is the Sun-Jupiter system. This system was especially useful since it contained two of the more difficult Poincare eigenvalue cases, the degenerate case and the imaginary eigenvalue case. The perturbation solution to the canonical modal variables was examined using both an expansion of the Hamiltonian and using a representation that was considered exact Both methods compared quite well for small perturbations to the initial condition. As expected, the expansion solution failed first due to truncation after the third order term of the expansion.

AFIT Designator

AFIT-GA-ENY-92D-03

DTIC Accession Number

ADA258970

Comments

The author's Vita page is omitted.

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