Title page for ETD etd-09082012-040238

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
  • Space trajectories
Date of Defense 1970-03-05
Availability restricted

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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