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Virginia Tech

Halphen's theorem and related results

Abstract

dc:description.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.

Degree

thesis:*
Name thesis:degree_name
Ph. D.
Level thesis:degree_level
doctoral
Discipline thesis:degree_discipline
Mathematics
Department dc:contributor.department
Mathematics
Grantor dc:publisher
Virginia Tech
Year dc:date.issued
1970

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Culbertson, George Edward
Chair dc:contributor.committeechair
  • Layman, John W.
Committee members dc:contributor.committeemember
  • Rutland, Leon W.
  • McFadden, Leonard D.
  • Patty, C. Wayne
  • DeCicco, John
  • Kramer, Clyde Y.
  • Williams, Clayton D.
  • Johnson, Harry Lee
  • Washenberger, James

Rights

dc:rights
Statement dc:rights
  • In Copyright
Language dc:language.iso
en

Identifiers

dc:identifier.*
Dc Identifier Other
etd-09082012-040238
OAI identifier oai:identifier
oai:vtechworks.lib.vt.edu:10919/39308

Chain of custody

source
Harvested from
Virginia Tech
Base URL
vtechworks.lib.vt.edu/oai/request
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
related terms
citation

Culbertson, George Edward. Halphen's theorem and related results. doctoral thesis, Virginia Tech, 1970. http://hdl.handle.net/10919/39308