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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Halphen's theorem and related results"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Layman, John W."],"dc:contributor.committeemember":["Rutland, Leon W.","McFadden, Leonard D.","Patty, C. 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