Date of Award:
Master of Science (MS)
Mathematics and Statistics
Basic concepts of differential geometry and Lie theory are introduced. Lie transformation groups are applied to linear systems of differential equations and the problem of describing rigid body orientation. Linear Hamiltonian systems are then treated as a Lie system of differential equations. This theory is applied to a particular Hamiltonian system arising from a problem in control theory, the linear state regulator problem.
Brannan, James R., "Interpretation and Application of Elements of Differential Geometry and Lie Theory" (1976). All Graduate Theses and Dissertations. 6952.