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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

The geometric discretisation of the Suslov problem: A case study of consistency for nonholonomic integrators
Pages: 4249 - 4275, Issue 8, August 2017

doi:10.3934/dcds.2017182      Abstract        References        Full text (2359.8K)           Related Articles

Luis C. García-Naranjo - Departamento de Matemáticas y Mecánica, IIMAS-UNAM, Apdo. Postal: 20-726, Mexico City, 01000, Mexico (email)
Fernando Jiménez - Department of Applied Mathematics, University of Waterloo, 200 Univ. Avenue West, N2L 3G1, Waterloo, Canada (email)

1 V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics; Dynamical Systems III, $3^{rd}$ edition, Encyclopaedia of Mathematical Sciences, 3. Springer-Verlag, Berlin, 2006.       
2 A. M. Bloch, Nonholonomic Mechanics and Control, $2^{nd}$ edition, Springer-Verlag, New York, 2015.       
3 A. I. Bobenko and Y. B. Suris, Discrete Lagrangian reduction, discrete Euler-Poincaré equations and semidirect products, Lett. Math. Phys., 49 (1999), 79-93.       
4 J. Cortés and S. Martínez, Nonholonomic integrators, Nonlinearity, 14 (2001), 1365-1392.       
5 Y. N. Fedorov and V. V. Kozlov, Various aspects of $n-$dimensional rigid body dynamics, Amer. Math. Soc. Transl., 168 (1995), 141-171.       
6 Y. N. Fedorov and D. V. Zenkov, Discrete nonholonomic LL systems on Lie groups, Nonlinearity, 18 (2005), 2211-2241.       
7 Y. N. Fedorov, A discretization of the nonholonomic Chaplygin sphere problem, SIGMA, 3 (2007), Paper 044, 15pp.       
8 Y. N. Fedorov, A. J. Maciejewski and M. Przybylska, The Poisson equations in the nonholonomic Suslov problem: Integrability, meromorphic and hypergeometric solutions, Nonlinearity, 22 (2009), 2231-2259.       
9 L. C. García-Naranjo, J. C. Marrero, A. J. Maciejewski and M. Przybylska, The inhomogeneous Suslov problem, Phys. Lett. A, 378 (2014), 2389-2394.       
10 D. Iglesias, J. C. Marrero, D. Martín de Diego and E. Martínez, Discrete nonholonomic Lagrangian systems on Lie groupoids, J. Nonlinear Sci., 18 (2008), 351-397.       
11 A. Iserles, H. Z. Munthe-Kaas, S. P. Norsett and A. Zanna, Lie-group methods, Acta Numerica, 9 (2000), 215-365.       
12 F. Jiménez and J. Scheurle, On the discretization of nonholonomic mechanics in $\mathbbR^n$, J. Geom. Mech., 7 (2015), 43-80.       
13 F. Jiménez and J. Scheurle, On the discretization of the Euler-Poincaré-Suslov equations in $SO(3)$, arXiv:1506.01289. To appear in J. Geom. Mech.
14 J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry. A Basic Exposition of Classical Mechanical Systems, $2^{nd}$ edition, Texts in Applied Mathematics, 17. Springer-Verlag, New York, 1999.       
15 J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numerica, 10 (2001), 357-514.       
16 R. McLachlan and M. Perlmutter, Integrators for nonholonomic mechanical systems, J. Nonlinear Sci., 16 (2006), 283-328.       
17 J. Moser and A. P. Veselov, Discrete versions of some classical integrable systems and factorization of matrix polynomials, Comm. Math. Phys., 139 (1991), 217-243.       
18 G. K. Suslov, Theoretical Mechanics, Gostekhizdat, Moscow, 1946 (in Russian).
19 A. P. Veselov, Integrable discrete-time systems and difference operators, Funct. Anal. Appl., 22 (1988), 1-13.       

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