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The ubiquity of the symplectic Hamiltonian equations in mechanics
$G$-Chaplygin systems with internal symmetries, truncation, and an (almost) symplectic view of Chaplygin's ball
1. | Section de Mathematiques, Station 8, EPFL, CH-1015 Lausanne, Switzerland, Switzerland |
[1] |
E. Minguzzi. A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena. Journal of Geometric Mechanics, 2015, 7 (4) : 473-482. doi: 10.3934/jgm.2015.7.473 |
[2] |
Panayotis G. Kevrekidis, Vakhtang Putkaradze, Zoi Rapti. Non-holonomic constraints and their impact on discretizations of Klein-Gordon lattice dynamical models. Conference Publications, 2015, 2015 (special) : 696-704. doi: 10.3934/proc.2015.0696 |
[3] |
Luis García-Naranjo. Reduction of almost Poisson brackets and Hamiltonization of the Chaplygin sphere. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 37-60. doi: 10.3934/dcdss.2010.3.37 |
[4] |
Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 |
[5] |
Andrey Tsiganov. Integrable Euler top and nonholonomic Chaplygin ball. Journal of Geometric Mechanics, 2011, 3 (3) : 337-362. doi: 10.3934/jgm.2011.3.337 |
[6] |
Michał Jóźwikowski, Witold Respondek. A comparison of vakonomic and nonholonomic dynamics with applications to non-invariant Chaplygin systems. Journal of Geometric Mechanics, 2019, 11 (1) : 77-122. doi: 10.3934/jgm.2019005 |
[7] |
Domokos Szász. Algebro-geometric methods for hard ball systems. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 427-443. doi: 10.3934/dcds.2008.22.427 |
[8] |
Chenchen Mou. Nonlinear elliptic systems involving the fractional Laplacian in the unit ball and on a half space. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2335-2362. doi: 10.3934/cpaa.2015.14.2335 |
[9] |
Mikhail B. Sevryuk. Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 569-595. doi: 10.3934/dcds.2007.18.569 |
[10] |
Xiaocai Wang, Junxiang Xu. Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 701-718. doi: 10.3934/dcds.2009.25.701 |
[11] |
Tiago Carvalho, Luiz Fernando Gonçalves. A flow on $ S^2 $ presenting the ball as its minimal set. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020287 |
[12] |
Ziyi Cai, Haiyang He. Asymptotic behavior of solutions for nonlinear integral equations with Hénon type on the unit Ball. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4349-4362. doi: 10.3934/cpaa.2020196 |
[13] |
Dongfeng Zhang, Junxiang Xu. On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 635-655. doi: 10.3934/dcds.2006.16.635 |
[14] |
Huawen Ye, Honglei Xu. Global stabilization for ball-and-beam systems via state and partial state feedback. Journal of Industrial & Management Optimization, 2016, 12 (1) : 17-29. doi: 10.3934/jimo.2016.12.17 |
[15] |
Yuri N. Fedorov, Dmitry V. Zenkov. Dynamics of the discrete Chaplygin sleigh. Conference Publications, 2005, 2005 (Special) : 258-267. doi: 10.3934/proc.2005.2005.258 |
[16] |
Hahng-Yun Chu, Se-Hyun Ku, Jong-Suh Park. Conley's theorem for dispersive systems. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 313-321. doi: 10.3934/dcdss.2015.8.313 |
[17] |
Artur O. Lopes, Elismar R. Oliveira. Entropy and variational principles for holonomic probabilities of IFS. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 937-955. doi: 10.3934/dcds.2009.23.937 |
[18] |
Luca Consolini, Alessandro Costalunga, Manfredi Maggiore. A coordinate-free theory of virtual holonomic constraints. Journal of Geometric Mechanics, 2018, 10 (4) : 467-502. doi: 10.3934/jgm.2018018 |
[19] |
Alicia Cordero, José Martínez Alfaro, Pura Vindel. Bott integrable Hamiltonian systems on $S^{2}\times S^{1}$. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 587-604. doi: 10.3934/dcds.2008.22.587 |
[20] |
Marko Nedeljkov, Sanja Ružičić. On the uniqueness of solution to generalized Chaplygin gas. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4439-4460. doi: 10.3934/dcds.2017190 |
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