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Energy conserving nonholonomic integrators
1. | Coordinated Science Laboratory, University of Illnois at Urbana-Champaign, 1308 W. Main St., IL 61801, United States |
[1] |
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 |
[2] |
Jean-Marie Souriau. On Geometric Mechanics. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 595-607. doi: 10.3934/dcds.2007.19.595 |
[3] |
Andrew D. Lewis. Nonholonomic and constrained variational mechanics. Journal of Geometric Mechanics, 2020, 12 (2) : 165-308. doi: 10.3934/jgm.2020013 |
[4] |
Andrew D. Lewis. Erratum for "nonholonomic and constrained variational mechanics". Journal of Geometric Mechanics, 2020, 12 (4) : 671-675. doi: 10.3934/jgm.2020033 |
[5] |
Gianne Derks. Book review: Geometric mechanics. Journal of Geometric Mechanics, 2009, 1 (2) : 267-270. doi: 10.3934/jgm.2009.1.267 |
[6] |
Andrew D. Lewis. The physical foundations of geometric mechanics. Journal of Geometric Mechanics, 2017, 9 (4) : 487-574. doi: 10.3934/jgm.2017019 |
[7] |
Marin Kobilarov, Jerrold E. Marsden, Gaurav S. Sukhatme. Geometric discretization of nonholonomic systems with symmetries. Discrete and Continuous Dynamical Systems - S, 2010, 3 (1) : 61-84. doi: 10.3934/dcdss.2010.3.61 |
[8] |
François Gay-Balmaz, Darryl D. Holm. Predicting uncertainty in geometric fluid mechanics. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1229-1242. doi: 10.3934/dcdss.2020071 |
[9] |
Sebastián J. Ferraro, David Iglesias-Ponte, D. Martín de Diego. Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods. Conference Publications, 2009, 2009 (Special) : 220-229. doi: 10.3934/proc.2009.2009.220 |
[10] |
Kurt Ehlers. Geometric equivalence on nonholonomic three-manifolds. Conference Publications, 2003, 2003 (Special) : 246-255. doi: 10.3934/proc.2003.2003.246 |
[11] |
Manuel de León, Víctor M. Jiménez, Manuel Lainz. Contact Hamiltonian and Lagrangian systems with nonholonomic constraints. Journal of Geometric Mechanics, 2021, 13 (1) : 25-53. doi: 10.3934/jgm.2021001 |
[12] |
Waldyr M. Oliva, Gláucio Terra. Improving E. Cartan considerations on the invariance of nonholonomic mechanics. Journal of Geometric Mechanics, 2019, 11 (3) : 439-446. doi: 10.3934/jgm.2019022 |
[13] |
Alexis Arnaudon, So Takao. Networks of coadjoint orbits: From geometric to statistical mechanics. Journal of Geometric Mechanics, 2019, 11 (4) : 447-485. doi: 10.3934/jgm.2019023 |
[14] |
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 |
[15] |
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 |
[16] |
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 |
[17] |
Thomas Hagen, Andreas Johann, Hans-Peter Kruse, Florian Rupp, Sebastian Walcher. Dynamical systems and geometric mechanics: A special issue in Honor of Jürgen Scheurle. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : i-iii. doi: 10.3934/dcdss.20204i |
[18] |
Juan Carlos Marrero, David Martín de Diego, Ari Stern. Symplectic groupoids and discrete constrained Lagrangian mechanics. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 367-397. doi: 10.3934/dcds.2015.35.367 |
[19] |
Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159 |
[20] |
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 |
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