The role of pseudo-hypersurfaces in non-holonomic motion

David Delphenich; David Delphenich

doi:10.3934/math.2020307

AIMS Mathematics

2020, Volume 5, Issue 5: 4793-4829. doi: 10.3934/math.2020307

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Research article

The role of pseudo-hypersurfaces in non-holonomic motion

David Delphenich ^,

Independent researcher, 1830 SR 725, Spring Valley, OH USA 45370

Received: 09 September 2019 Accepted: 20 April 2020 Published: 02 June 2020
MSC : 14J81, 37J60, 53A07, 53A17, 53B50, 58A17, 70F25

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.
- non-holonomic constraints,
- Pfaff equation,
- geometry of hypersurfaces,
- integrability of differential systems,
- Lorentz equation,
- mechanics and differential forms
Citation: David Delphenich. The role of pseudo-hypersurfaces in non-holonomic motion[J]. AIMS Mathematics, 2020, 5(5): 4793-4829. doi: 10.3934/math.2020307

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Abstract

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.

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