Controlled Lagrangians and Stabilization of Euler-Poincaré Mechanical Systems with Broken Symmetry

dc.contributor.advisorOhsawa, Tomoki
dc.creatorContreras, Cesar
dc.date.accessioned2021-12-08T13:53:32Z
dc.date.available2021-12-08T13:53:32Z
dc.date.created2021-05
dc.date.issued2021-02-26
dc.date.submittedMay 2021
dc.date.updated2021-12-08T13:53:35Z
dc.description.abstractWe extend the method of Controlled Lagrangians to Euler-Poincaré mechanical systems with broken symmetry, and find asymptotic stabilizing controls of unstable equilibria of such mechanical systems. Our motivating example is a top spinning on a movable base: The gravity breaks the symmetry with respect to the three-dimensional rotations and translations of the system, and also renders the upright spinning equilibrium unstable. We formulate the system as Euler-Poincaré equations with advected parameters using semidirect Lie group $\mathsf{SE}(3) \ltimes (\mathbb{R}^{4})^*$, and find a control that is applied to the base to asymptotically stabilize the equilibrium.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10735.1/9286
dc.language.isoen
dc.subjectEuler characteristic
dc.subjectLagrange equations
dc.subjectBroken symmetry (Physics)
dc.subjectEquilibrium
dc.titleControlled Lagrangians and Stabilization of Euler-Poincaré Mechanical Systems with Broken Symmetry
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.levelDoctoral
thesis.degree.namePHD

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