Abstract:
The rolling of a dynamically balanced ball on a horizontal rough table without slipping was described by Chaplygin using Abel quadratures. We discuss integrable discretizations and deformations of this nonholonomic system using the same Abel quadratures. As a by-product one gets a new geodesic flow on the unit two-dimensional sphere whose additional integrals of motion are polynomials in the momenta of fourth order.
Keywords:
nonholonomic systems, Abel quadratures, arithmetic of divisors.
Citation:
Andrey V. Tsiganov, “Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball”, Regul. Chaotic Dyn., 22:4 (2017), 353–367
\Bibitem{Tsi17}
\by Andrey V. Tsiganov
\paper Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 4
\pages 353--367
\mathnet{http://mi.mathnet.ru/rcd260}
\crossref{https://doi.org/10.1134/S1560354717040025}
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Linking options:
https://www.mathnet.ru/eng/rcd260
https://www.mathnet.ru/eng/rcd/v22/i4/p353
This publication is cited in the following 12 articles:
Andrey V. Tsiganov, “Equivalent Integrable Metrics on the Sphere with Quartic Invariants”, SIGMA, 18 (2022), 094, 19 pp.
A. V. Tsiganov, “Discretization and superintegrability all rolled into one”, Nonlinearity, 33:9 (2020), 4924–4939
B. Gajić, B. Jovanović, “Two Integrable Cases of a Ball Rolling over a Sphere in $\mathbb{R}^n$”, Rus. J. Nonlin. Dyn., 15:4 (2019), 457–475
Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186
A. V. Borisov, A. V. Tsyganov, “Vliyanie effektov Barnetta-Londona i Einshteina-de Gaaza na dvizhenie negolonomnoi sfery Rausa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 583–598
A. V. Tsiganov, “Elliptic curve arithmetic and superintegrable systems”, Phys. Scr., 94:8 (2019), 085207
B. Gajic, B. Jovanovic, “Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere”, Nonlinearity, 32:5 (2019), 1675–1694
A. V. Tsiganov, “Backlund transformations and divisor doubling”, J. Geom. Phys., 126:SI (2018), 148–158
A. V. Tsiganov, “Duffing Oscillator and Elliptic Curve Cryptography”, Nelin. Dinam., 14:2 (2018), 235–241
A. V. Tsiganov, “Discretization of Hamiltonian systems and intersection theory”, Theoret. and Math. Phys., 197:3 (2018), 1806–1822
Andrey V. Tsiganov, “On Discretization of the Euler Top”, Regul. Chaotic Dyn., 23:6 (2018), 785–796
A. V. Tsiganov, “On exact discretization of cubic-quintic Duffing oscillator”, J. Math. Phys., 59:7 (2018), 072703
Citation in format AMSBIB
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