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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-06-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020307/fulltext.html |
| _version_ | 1818259426956541952 |
|---|---|
| author | David Delphenich |
| author_facet | David Delphenich |
| author_sort | David Delphenich |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-12T18:15:16Z |
| format | Article |
| id | doaj.art-c685d4c6a8314e6b911bb09c31eb4fcb |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T18:15:16Z |
| publishDate | 2020-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c685d4c6a8314e6b911bb09c31eb4fcb2022-12-22T00:16:18ZengAIMS 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 |
| 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 |
| title | 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_short | The role of pseudo-hypersurfaces in non-holonomic motion |
| title_sort | role of pseudo hypersurfaces in non holonomic motion |
| 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 |
| work_keys_str_mv | AT daviddelphenich theroleofpseudohypersurfacesinnonholonomicmotion AT daviddelphenich roleofpseudohypersurfacesinnonholonomicmotion |