The role of pseudo-hypersurfaces in non-holonomic motion

被引：0
|
作者：
Delphenich, David [1 ]
机构：
[1] 1830 SR 725, Spring Valley, OH 45370 USA
来源：
AIMS MATHEMATICS | 2020年 / 5卷 / 05期
关键词：
non-holonomic constraints; Pfaff equation; geometry of hypersurfaces; integrability of differential systems; Lorentz equation; mechanics and differential forms;
D O I：
10.3934/math.2020307
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：4793 / 4829
页数：37
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