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Geometric equivalence on nonholonomic three-manifolds

Pages: 246 - 255, Issue Special, July 2003

 Abstract        Full Text (194.1K)              

Kurt Ehlers - Truckee Meadows Community College, 7000 Dandini Blvd, Reno, NV 89512, United States (email)

Abstract: We apply Cartan’s method of equivalence to the case of nonholonomic geometry on three-dimensional contact manifolds. Our main result is to derive the differential invariants for these structures and give geometric interpretations. We show that the symmetry group of such a structure has dimension at most four. Our motivation is to study the geometry associated with classical mechanical systems with nonholonomic constraints.

Keywords:  Nonholonomic mechanics, equivalence method, G-structures.
Mathematics Subject Classification:  Primary: 70G45,53C10,37J60; Secondary: 58A17.

Received: September 2002;      Revised: April 2003;      Published: April 2003.