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Reduction of almost Poisson brackets and Hamiltonization of the Chaplygin sphere
Geometric discretization of nonholonomic systems with symmetries
1. | California Institute of Technology, Control and Dynamical Systems, Pasadena, CA 91125, United States |
2. | Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, United States |
3. | University of Southern California, Robotic Embedded Systems Laboratory, Los Angeles, California 90089-2905, United States |
[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] |
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 |
[3] |
Andrew D. Lewis. Nonholonomic and constrained variational mechanics. Journal of Geometric Mechanics, 2020, 12 (2) : 165-308. doi: 10.3934/jgm.2020013 |
[4] |
Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of nonholonomic discrete mechanical systems by stages. Journal of Geometric Mechanics, 2020, 12 (4) : 607-639. doi: 10.3934/jgm.2020029 |
[5] |
Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of nonholonomic discrete mechanical systems. Journal of Geometric Mechanics, 2010, 2 (1) : 69-111. doi: 10.3934/jgm.2010.2.69 |
[6] |
Andrew D. Lewis. Erratum for "nonholonomic and constrained variational mechanics". Journal of Geometric Mechanics, 2020, 12 (4) : 671-675. doi: 10.3934/jgm.2020033 |
[7] |
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 |
[8] |
Jorge Cortés. Energy conserving nonholonomic integrators. Conference Publications, 2003, 2003 (Special) : 189-199. doi: 10.3934/proc.2003.2003.189 |
[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] |
Andrey Tsiganov. Poisson structures for two nonholonomic systems with partially reduced symmetries. Journal of Geometric Mechanics, 2014, 6 (3) : 417-440. doi: 10.3934/jgm.2014.6.417 |
[11] |
Božzidar Jovanović. Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems. Journal of Geometric Mechanics, 2018, 10 (2) : 173-187. doi: 10.3934/jgm.2018006 |
[12] |
Paul Popescu, Cristian Ida. Nonlinear constraints in nonholonomic mechanics. Journal of Geometric Mechanics, 2014, 6 (4) : 527-547. doi: 10.3934/jgm.2014.6.527 |
[13] |
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 |
[14] |
Sergio Grillo, Marcela Zuccalli. Variational reduction of Lagrangian systems with general constraints. Journal of Geometric Mechanics, 2012, 4 (1) : 49-88. doi: 10.3934/jgm.2012.4.49 |
[15] |
Luis C. García-Naranjo, Mats Vermeeren. Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics. Journal of Computational Dynamics, 2021, 8 (3) : 241-271. doi: 10.3934/jcd.2021011 |
[16] |
Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of discrete mechanical systems by stages. Journal of Geometric Mechanics, 2016, 8 (1) : 35-70. doi: 10.3934/jgm.2016.8.35 |
[17] |
B. Cantó, C. Coll, A. Herrero, E. Sánchez, N. Thome. Pole-assignment of discrete time-delay systems with symmetries. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 641-649. doi: 10.3934/dcdsb.2006.6.641 |
[18] |
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 |
[19] |
Viviana Alejandra Díaz, David Martín de Diego. Generalized variational calculus for continuous and discrete mechanical systems. Journal of Geometric Mechanics, 2018, 10 (4) : 373-410. doi: 10.3934/jgm.2018014 |
[20] |
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 |
2020 Impact Factor: 2.425
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