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This article is cited in 17 scientific papers (total in 17 papers)
Dynamics of billiards
The Wagner Curvature Tenzor in Nonholonomic Mechanics
V. Dragovićab, B. Gajićb a SISSA, Trieste, Italy
b Mathematical Institute, Belgrade, Yugoslavia
Abstract:
We present the classical Wagner construction from 1935 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.
Received: 15.01.2003
Citation:
V. Dragović, B. Gajić, “The Wagner Curvature Tenzor in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 8:1 (2003), 105–123
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https://www.mathnet.ru/eng/rcd769 https://www.mathnet.ru/eng/rcd/v8/i1/p105
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