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Geometric Mechanics and Control

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title
Geometric Mechanics and Control
author
Turnage, John Michael
abstract
We present a study of the optimal time of flight of a vertical rolling disk on a surface of revolution. This is a twist on the classic problem of a disk rolling without slipping on the plane, which is a canonical example of a nonholonomic dynamical system. Such systems are characterized by the presence of non-integrable constraints on the velocities, which results in path-dependent behavior. Geometrically, these constraints appear as a distribution on the tangent bundle to the configuration manifold of the system. Optimal control problems on such systems are particularly interesting, since the distribution is non-involutive. Briefly, this means that the distribution defined by the nonholonomic constraints is not closed under the Lie bracket operation on a set of spanning vector-fields. This lack of closure results in a larger attainable set of configurations than would be possible if one only naively considered integral curves along the generalized coordinate curves.
contributor
Gemmer, John A. (committee chair)
Parsley, Jason (committee member)
Moore, Frank (committee member)
date
2022-05-24T08:35:55Z (accessioned)
2022-05-24T08:35:55Z (available)
2022 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/100729 (uri)
language
en (iso)
publisher
Wake Forest University
type
Thesis

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