Halphen's theorem and related results

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dc.contributor.authorCulbertson, George Edwarden
dc.contributor.committeechairLayman, John W.en
dc.contributor.committeememberRutland, Leon W.en
dc.contributor.committeememberMcFadden, Leonard D.en
dc.contributor.committeememberPatty, C. Wayneen
dc.contributor.committeememberDeCicco, Johnen
dc.contributor.committeememberKramer, Clyde Y.en
dc.contributor.committeememberWilliams, Clayton D.en
dc.contributor.committeememberJohnson, Harry Leeen
dc.contributor.committeememberWashenberger, Jamesen
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:18:30Zen
dc.date.adate2012-09-08en
dc.date.available2014-03-14T21:18:30Zen
dc.date.issued1970-03-05en
dc.date.rdate2012-09-08en
dc.date.sdate2012-09-08en
dc.description.abstractHalphen's Theorem states that, "A necessary and sufficient condition for every dynamical trajectory in a positional field of force in E3 to be planar is that the field of force is either parallel or central." This result has been known for some time, however only the sufficiency part of the theorem is widely documented. A new analytic proof of the necessity part of Halphen's Theorem was developed. The details of this proof motivated the new concepts of a flat point in a field of force and a flat point on a dynamical trajectory in a positional field of force.en
dc.description.degreePh. D.en
dc.format.extentvii, 120 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-09082012-040238en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-09082012-040238/en
dc.identifier.urihttp://hdl.handle.net/10919/39308en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1970.C8.pdfen
dc.relation.isformatofOCLC# 11598325en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1970.C8en
dc.subject.lcshCurves, Planeen
dc.subject.lcshSpace trajectoriesen
dc.titleHalphen's theorem and related resultsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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