The role of pseudo-hypersurfaces in non-holonomic motion
The geometry of hypersurfaces is generalized to pseudo-hypersurfaces, which are defined by Pfaff equations. The general methods are then applied to modeling the kinematics of motion constrained by a single linear, non-holonomic constraint. They are then applied to the example of a charge moving in a...
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AIMS Press
2020-06-01
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020307/fulltext.html |
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doaj-c685d4c6a8314e6b911bb09c31eb4fcb2020-11-25T03:54:41ZengAIMS PressAIMS Mathematics2473-69882020-06-01554793482910.3934/math.2020307The role of pseudo-hypersurfaces in non-holonomic motionDavid Delphenich0Independent researcher, 1830 SR 725, Spring Valley, OH USA 45370The geometry of hypersurfaces is generalized to pseudo-hypersurfaces, which are defined by Pfaff equations. The general methods are then applied to modeling the kinematics of motion constrained by a single linear, non-holonomic constraint. They are then applied to the example of a charge moving in an electromagnetic field, and the Lorentz equation of motion is shown to represent a geodesic that is constrained to lie in a pseudo-hypersurface that is defined by the potential 1-form.https://www.aimspress.com/article/10.3934/math.2020307/fulltext.htmlnon-holonomic constraintspfaff equationgeometry of hypersurfacesintegrability of differential systemslorentz equationmechanics and differential forms |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
David Delphenich |
| spellingShingle |
David Delphenich The role of pseudo-hypersurfaces in non-holonomic motion AIMS Mathematics non-holonomic constraints pfaff equation geometry of hypersurfaces integrability of differential systems lorentz equation mechanics and differential forms |
| author_facet |
David Delphenich |
| author_sort |
David Delphenich |
| title |
The role of pseudo-hypersurfaces in non-holonomic motion |
| title_short |
The role of pseudo-hypersurfaces in non-holonomic motion |
| title_full |
The role of pseudo-hypersurfaces in non-holonomic motion |
| title_fullStr |
The role of pseudo-hypersurfaces in non-holonomic motion |
| title_full_unstemmed |
The role of pseudo-hypersurfaces in non-holonomic motion |
| title_sort |
role of pseudo-hypersurfaces in non-holonomic motion |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2020-06-01 |
| description |
The geometry of hypersurfaces is generalized to pseudo-hypersurfaces, which are defined by Pfaff equations. The general methods are then applied to modeling the kinematics of motion constrained by a single linear, non-holonomic constraint. They are then applied to the example of a charge moving in an electromagnetic field, and the Lorentz equation of motion is shown to represent a geodesic that is constrained to lie in a pseudo-hypersurface that is defined by the potential 1-form. |
| topic |
non-holonomic constraints pfaff equation geometry of hypersurfaces integrability of differential systems lorentz equation mechanics and differential forms |
| url |
https://www.aimspress.com/article/10.3934/math.2020307/fulltext.html |
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AT daviddelphenich theroleofpseudohypersurfacesinnonholonomicmotion AT daviddelphenich roleofpseudohypersurfacesinnonholonomicmotion |
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