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Bidifferential graded algebras and integrable systems
Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods
1. | Departamento de Mateemática and Instituto de Matemática Bahía Blanca, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca and CONICET, Argentina |
2. | Unidad asociada ULL-CSIC “Geometría Diferencial y Mecánica Geométrica”, Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain |
3. | Unidad Asociada ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Serrano 123, 28006 Madrid, Spain |
[1] |
Oscar E. Fernandez, Anthony M. Bloch, P. J. Olver. Variational Integrators for Hamiltonizable Nonholonomic Systems. Journal of Geometric Mechanics, 2012, 4 (2) : 137-163. doi: 10.3934/jgm.2012.4.137 |
[2] |
Jorge Cortés. Energy conserving nonholonomic integrators. Conference Publications, 2003, 2003 (Special) : 189-199. doi: 10.3934/proc.2003.2003.189 |
[3] |
Leonardo Colombo, Fernando Jiménez, David Martín de Diego. Variational integrators for mechanical control systems with symmetries. Journal of Computational Dynamics, 2015, 2 (2) : 193-225. doi: 10.3934/jcd.2015003 |
[4] |
Cédric M. Campos, Sina Ober-Blöbaum, Emmanuel Trélat. High order variational integrators in the optimal control of mechanical systems. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4193-4223. doi: 10.3934/dcds.2015.35.4193 |
[5] |
Pedro L. García, Antonio Fernández, César Rodrigo. Variational integrators for discrete Lagrange problems. Journal of Geometric Mechanics, 2010, 2 (4) : 343-374. doi: 10.3934/jgm.2010.2.343 |
[6] |
Werner Bauer, François Gay-Balmaz. Variational integrators for anelastic and pseudo-incompressible flows. Journal of Geometric Mechanics, 2019, 11 (4) : 511-537. doi: 10.3934/jgm.2019025 |
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Luis C. garcía-Naranjo, Fernando Jiménez. The geometric discretisation of the Suslov problem: A case study of consistency for nonholonomic integrators. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4249-4275. doi: 10.3934/dcds.2017182 |
[8] |
Claude Le Bris, Frédéric Legoll. Integrators for highly oscillatory Hamiltonian systems: An homogenization approach. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 347-373. doi: 10.3934/dcdsb.2010.13.347 |
[9] |
Matteo Focardi, Paolo Maria Mariano. Discrete dynamics of complex bodies with substructural dissipation: Variational integrators and convergence. Discrete and Continuous Dynamical Systems - B, 2009, 11 (1) : 109-130. doi: 10.3934/dcdsb.2009.11.109 |
[10] |
Mats Vermeeren. Modified equations for variational integrators applied to Lagrangians linear in velocities. Journal of Geometric Mechanics, 2019, 11 (1) : 1-22. doi: 10.3934/jgm.2019001 |
[11] |
Michele Zadra, Elizabeth L. Mansfield. Using Lie group integrators to solve two and higher dimensional variational problems with symmetry. Journal of Computational Dynamics, 2019, 6 (2) : 485-511. doi: 10.3934/jcd.2019025 |
[12] |
Michael Entov, Leonid Polterovich, Daniel Rosen. Poisson brackets, quasi-states and symplectic integrators. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1455-1468. doi: 10.3934/dcds.2010.28.1455 |
[13] |
Benedict Leimkuhler, Charles Matthews, Tiffany Vlaar. Partitioned integrators for thermodynamic parameterization of neural networks. Foundations of Data Science, 2019, 1 (4) : 457-489. doi: 10.3934/fods.2019019 |
[14] |
A. Alamo, J. M. Sanz-Serna. Word combinatorics for stochastic differential equations: Splitting integrators. Communications on Pure and Applied Analysis, 2019, 18 (4) : 2163-2195. doi: 10.3934/cpaa.2019097 |
[15] |
Fasma Diele, Carmela Marangi. Positive symplectic integrators for predator-prey dynamics. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2661-2678. doi: 10.3934/dcdsb.2017185 |
[16] |
Yong Chen, Hongjun Gao, María J. Garrido–Atienza, Björn Schmalfuss. Pathwise solutions of SPDEs driven by Hölder-continuous integrators with exponent larger than $1/2$ and random dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (1) : 79-98. doi: 10.3934/dcds.2014.34.79 |
[17] |
Andrew D. Lewis. Nonholonomic and constrained variational mechanics. Journal of Geometric Mechanics, 2020, 12 (2) : 165-308. doi: 10.3934/jgm.2020013 |
[18] |
Artur O. Lopes, Elismar R. Oliveira. Entropy and variational principles for holonomic probabilities of IFS. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 937-955. doi: 10.3934/dcds.2009.23.937 |
[19] |
Andrew D. Lewis. Erratum for "nonholonomic and constrained variational mechanics". Journal of Geometric Mechanics, 2020, 12 (4) : 671-675. doi: 10.3934/jgm.2020033 |
[20] |
Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 |
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