Abstract
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.
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
- Licence dc:rights.uri
- 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