The parametrically excited pendulum and the criteria for predicting the onset of chaos

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dc.contributor.authorHsu, Tseng-Hsingen
dc.contributor.committeechairHendricks, Scott L.en
dc.contributor.committeememberSmith, Charles W.en
dc.contributor.committeememberMook, Dean T.en
dc.contributor.departmentEngineering Mechanicsen
dc.date.accessioned2014-03-14T21:32:14Zen
dc.date.adate2009-03-24en
dc.date.available2014-03-14T21:32:14Zen
dc.date.issued1991-11-15en
dc.date.rdate2009-03-24en
dc.date.sdate2009-03-24en
dc.description.abstractA pendulum with its supporting point vibrating in both the x and the y direction is analyzed. Numerical simulation by computer is used to analyze the motion of the pendulum. Chaotic motion of the system is observed. Threshold values for chaos are obtained by simulation. The Lyapunov exponent and the fast Fourier transform ( FFT ) are used as the criteria to determine if the system is chaotic. Two predictive theoretical criteria, the Melnikov criterion and a period-doubling criterion, are then applied to the system. The results obtained by simulation and by theoretical criteria are shown to be in good agreement. A brute-force approach is used to supplement the results. It is found that the motion of this simple driven pendulum will have very complicated behavior. Multiple attractors can be shown to coexist.en
dc.description.degreeMaster of Scienceen
dc.format.extent61 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-03242009-040616en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03242009-040616/en
dc.identifier.urihttp://hdl.handle.net/10919/41763en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V855_1991.H78.pdfen
dc.relation.isformatofOCLC# 25498552en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V855 1991.H78en
dc.subject.lcshChaotic behavior in systemsen
dc.subject.lcshNonlinear mechanicsen
dc.subject.lcshPendulumen
dc.titleThe parametrically excited pendulum and the criteria for predicting the onset of chaosen
dc.typeThesisen
dc.type.dcmitypeTexten
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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