V. Dragović, B. Gajić, “The Wagner Curvature Tenzor in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 8:1 (2003), 105

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Regular and Chaotic Dynamics, 2003, Volume 8, Issue 1, Pages 105–123
DOI: https://doi.org/10.1070/RD2003v008n01ABEH000229 (Mi rcd769)

This article is cited in 17 scientific papers (total in 17 papers)

Dynamics of billiards

The Wagner Curvature Tenzor in Nonholonomic Mechanics

V. Dragović^ab, B. Gajić^b

^a SISSA, Trieste, Italy
^b Mathematical Institute, Belgrade, Yugoslavia

Citations (17)

DOI: https://doi.org/10.1070/RD2003v008n01ABEH000229

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

Bibliographic databases:

Document Type: Article

MSC: 37J05, 37J60

Language: English

Citation: V. Dragović, B. Gajić, “The Wagner Curvature Tenzor in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 8:1 (2003), 105–123

Citation in format AMSBIB

\Bibitem{DraGaj03}

\by V. Dragovi\'c, B. Gaji\'c

\paper The Wagner Curvature Tenzor in Nonholonomic Mechanics

\jour Regul. Chaotic Dyn.

\yr 2003

\vol 8

\issue 1

\pages 105--123

\mathnet{http://mi.mathnet.ru/rcd769}

\crossref{https://doi.org/10.1070/RD2003v008n01ABEH000229}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1963972}

\zmath{https://zbmath.org/?q=an:1023.37036}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2003RCD.....8..105D}

Linking options:

https://www.mathnet.ru/eng/rcd769

https://www.mathnet.ru/eng/rcd/v8/i1/p105

This publication is cited in the following 17 articles:

Barrett I D., Remsing C.C., “On the Schouten and Wagner Curvature Tensors”, Rend. Circ. Mat. Palermo, 2021
Barrett I D., Remsing C.C., “Restricted Jacobi Fields”, Int. Electron. J. Geom., 14:2 (2021), 247–265
Alekseevsky D., “Shortest and Straightest Geodesics in Sub-Riemannian Geometry”, J. Geom. Phys., 155 (2020), 103713
Kurt M. Ehlers, Jair Koiller, “Cartan meets Chaplygin”, Theor. Appl. Mech., 46:1 (2019), 15–46
Oliva W.M., Terra G., “Improving E. Cartan Considerations on the Invariance of Nonholonomic Mechanics”, J. Geom. Mech., 11:3 (2019), 439–446
Barrett I D., Remsing C.C., “A Note on Flat Nonholonomic Riemannian Structures on Three-Dimensional Lie Groups”, Beitr. Algebr. Geom., 60:3 (2019), 419–436
Gajic B. Jovanovic B., “Nonholonomic Connections, Time Reparametrizations, and Integrability of the Rolling Ball Over a Sphere”, Nonlinearity, 32:5 (2019), 1675–1694
Alekseevsky D., Medvedev A., Slovak J., “Constant Curvature Models in Sub-Riemannian Geometry”, J. Geom. Phys., 138 (2019), 241–256
Barrett I D., Remsing C.C., “On Geodesic Invariance and Curvature in Nonholonomic Riemannian Geometry”, Publ. Math.-Debr., 94:1-2 (2019), 197–213
Božidar Jovanović, “Rolling balls over spheres in $\newcommand{\m}{\mathfrak m} {\mathbb{R}^n}$ ”, Nonlinearity, 31:9 (2018), 4006
Dennis I. Barrett, Rory Biggs, Claudiu C. Remsing, Olga Rossi, “Invariant nonholonomic Riemannian structures on three-dimensional Lie groups”, JGM, 8:2 (2016), 139
Xian Guo, ShuGen Ma, Bin Li, MingHui Wang, 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), 2014, 582
O. E. Fernandez, A. M. Bloch, “The Weitzenböck connection and time reparameterization in nonholonomic mechanics”, Journal of Mathematical Physics, 52:1 (2011)
SABRINA CASANOVA, ORCHIDEA MARIA LECIAN, GIOVANNI MONTANI, REMO RUFFINI, ROUSTAM ZALALETDINOV, “EXTENDED SCHOUTEN CLASSIFICATION FOR NON-RIEMANNIAN GEOMETRIES”, Mod. Phys. Lett. A, 23:01 (2008), 17
P. Ya. Grozman, D. A. Leites, “Nonholonomic Riemann and Weyl tensors for flag manifolds”, Theoret. and Math. Phys., 153:2 (2007), 1511–1538
Aurel Bejancu, “On the geometry of nonholonomic mechanical systems with vertical distribution”, Journal of Mathematical Physics, 48:5 (2007)
D. A. Leites, “On computer-aided solving differential equations and stability study of markets”, J. Math. Sci. (N. Y.), 133:4 (2006), 1464–1476

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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