|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||The Wagner curvature tensor in nonholonomic mechanics||Journal:||Regular and Chaotic Dynamics||Volume:||8||Issue:||1||First page:||105||Last page:||123||Issue Date:||1-Jan-2003||ISSN:||1560-3547||DOI:||10.1070/RD2003v008n01ABEH000229||Abstract:||
We present the classical Wagner construction from 19.35 of the curvature tensor for the completely nonholonomic manifolds in both invariant and coordinate way. The starting point is the Shouten curvature tensor for the nonholonomic connection introduced by Vranceanu and Shouten. We illustrate the construction by two mechanical examples: the case of a homogeneous disc rolling without sliding on a horizontal plane and the case of a homogeneous ball rolling without sliding on a fixed sphere. In the second case we study the conditions imposed on the ratio of diameters of the ball and the sphere to obtain a flat space - with the Wagner curvature tensor equal to zero.
|Publisher:||Springer Link||Project:||Geometry and Topology of Manifolds and Integrable Dynamical Systems|
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