Type of Document Dissertation Author Culbertson, George Edward URN etd-09082012-040238 Title Halphen's theorem and related results. Degree PhD Department Mathematics Advisory Committee
Advisor Name Title Layman, John W. Committee Chair DeCicco, John Committee Member Johnson, Harry Lee Committee Member Kramer, Clyde Y. Committee Member McFadden, Leonard D. Committee Member Patty, C. Wayne Committee Member Rutland, Leon W. Committee Member Washenberger, James Committee Member Williams, Clayton D. Committee Member Keywords
- Space trajectories
Date of Defense 1970-03-05 Availability restricted Abstract
Halphen'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.
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