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Interpretation And Application Of Elements Of Differential Geometry And Lie Theory, James R. Brannan
Interpretation And Application Of Elements Of Differential Geometry And Lie Theory, James R. Brannan
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
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.