Stabilization of Nonholonomic Euler–poincaré Mechanical Systems With Broken Symmetry by Controlled Lagrangians

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dc.contributor.advisorOhsawa, Tomoki
dc.contributor.advisorStelling, Allison
dc.contributor.committeeMemberDragovic, Vladimir
dc.contributor.committeeMemberRamakrishna, Viswanath
dc.contributor.committeeMemberPereira, L. Felipe
dc.creatorGarcia, Jorge Silva
dc.date.accessioned2023-05-25T19:47:10Z
dc.date.available2023-05-25T19:47:10Z
dc.date.created2022-12
dc.date.issued2022-12-01T06:00:00.000Z
dc.date.submittedDecember 2022
dc.date.updated2023-05-25T19:47:11Z
dc.description.abstractWe extend the method of Controlled Lagrangians to nonholonomic Euler–Poincaré mechanical systems with broken symmetry by considering the problem of stabilizing what we call a pendulum skate, a simple model of a figure skater developed by Gzenda and Putkaradze. By exploiting the symmetry of the system as well as taking care of the part of the symmetry broken by the gravity, the equations of motion are given as nonholonomic Euler–Poincaré equation with advected parameters. After that, we discovered the general form of the equilibrium points and presented the classification of two special ones, designated as sliding and spinning. Of our main interest is the stability of the sliding and spinning equilibria of the system. We show that the former is unstable and the latter is stable only under certain conditions. We use the method of Controlled Lagrangians to find a control to stabilize the sliding equilibrium and also show how to achieve the stabilization for the general equilibrium point.
dc.format.mimetypeapplication/pdf
dc.identifier.uri
dc.identifier.urihttps://hdl.handle.net/10735.1/9703
dc.language.isoen
dc.subjectMathematics
dc.titleStabilization of Nonholonomic Euler–poincaré Mechanical Systems With Broken Symmetry by Controlled Lagrangians
dc.typeThesis
dc.type.materialtext
thesis.degree.collegeSchool of Natural Sciences and Mathematics
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.namePHD

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