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Nonholonomic Lagrangian systems on Lie algebroids
1. | Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093, United States |
2. | Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, 28006 Madrid, Spain |
3. | Departamento de Matemática Fundamental, Unidad Asociada ULL-CSIC Geometría Diferencial y Mecánica Geométrica, Universidad de la Laguna, Tenerife, Canary Islands, Spain |
4. | IUMA and Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain |
[1] |
Hernán Cendra, Viviana A. Díaz. Lagrange-d'alembert-poincaré equations by several stages. Journal of Geometric Mechanics, 2018, 10 (1) : 1-41. doi: 10.3934/jgm.2018001 |
[2] |
Luca Biasco, Luigi Chierchia. Exponential stability for the resonant D'Alembert model of celestial mechanics. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 569-594. doi: 10.3934/dcds.2005.12.569 |
[3] |
Melvin Leok, Diana Sosa. Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on Lie algebroids. Journal of Geometric Mechanics, 2012, 4 (4) : 421-442. doi: 10.3934/jgm.2012.4.421 |
[4] |
K. C. H. Mackenzie. Drinfel'd doubles and Ehresmann doubles for Lie algebroids and Lie bialgebroids. Electronic Research Announcements, 1998, 4: 74-87. |
[5] |
José F. Cariñena, Irina Gheorghiu, Eduardo Martínez. Jacobi fields for second-order differential equations on Lie algebroids. Conference Publications, 2015, 2015 (special) : 213-222. doi: 10.3934/proc.2015.0213 |
[6] |
Andrew D. Lewis. Nonholonomic and constrained variational mechanics. Journal of Geometric Mechanics, 2020, 12 (2) : 165-308. doi: 10.3934/jgm.2020013 |
[7] |
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 |
[8] |
Dennise García-Beltrán, José A. Vallejo, Yurii Vorobiev. Lie algebroids generated by cohomology operators. Journal of Geometric Mechanics, 2015, 7 (3) : 295-315. doi: 10.3934/jgm.2015.7.295 |
[9] |
Andrew D. Lewis. Erratum for "nonholonomic and constrained variational mechanics". Journal of Geometric Mechanics, 2020, 12 (4) : 671-675. doi: 10.3934/jgm.2020033 |
[10] |
Robert I. McLachlan, Ander Murua. The Lie algebra of classical mechanics. Journal of Computational Dynamics, 2019, 6 (2) : 345-360. doi: 10.3934/jcd.2019017 |
[11] |
Giovanni De Matteis, Gianni Manno. Lie algebra symmetry analysis of the Helfrich and Willmore surface shape equations. Communications on Pure and Applied Analysis, 2014, 13 (1) : 453-481. doi: 10.3934/cpaa.2014.13.453 |
[12] |
Miguel Rodríguez-Olmos. Book review: Geometric mechanics and symmetry, by Darryl D. Holm, Tanya Schmah and Cristina Stoica. Journal of Geometric Mechanics, 2009, 1 (4) : 483-488. doi: 10.3934/jgm.2009.1.483 |
[13] |
Eduardo Martínez. Classical field theory on Lie algebroids: Multisymplectic formalism. Journal of Geometric Mechanics, 2018, 10 (1) : 93-138. doi: 10.3934/jgm.2018004 |
[14] |
Eduardo Martínez. Higher-order variational calculus on Lie algebroids. Journal of Geometric Mechanics, 2015, 7 (1) : 81-108. doi: 10.3934/jgm.2015.7.81 |
[15] |
Madeleine Jotz Lean, Kirill C. H. Mackenzie. Transitive double Lie algebroids via core diagrams. Journal of Geometric Mechanics, 2021, 13 (3) : 403-457. doi: 10.3934/jgm.2021023 |
[16] |
Juan Carlos Marrero, D. Martín de Diego, Diana Sosa. Variational constrained mechanics on Lie affgebroids. Discrete and Continuous Dynamical Systems - S, 2010, 3 (1) : 105-128. doi: 10.3934/dcdss.2010.3.105 |
[17] |
Katarzyna Grabowska, Marcin Zając. The Tulczyjew triple in mechanics on a Lie group. Journal of Geometric Mechanics, 2016, 8 (4) : 413-435. doi: 10.3934/jgm.2016014 |
[18] |
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 |
[19] |
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 |
[20] |
Dmitry V. Zenkov. Linear conservation laws of nonholonomic systems with symmetry. Conference Publications, 2003, 2003 (Special) : 967-976. doi: 10.3934/proc.2003.2003.967 |
2021 Impact Factor: 1.588
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