Authors: Dragović, Vladimir 
Gajić, Borislav 
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
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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