Research article

The role of pseudo-hypersurfaces in non-holonomic motion

  • 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.

    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

    Related Papers:

  • 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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