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Indices of singularities of robustly transitive sets
A new problem of adiabatic invariance related to the rigid body dynamics
1. | Università di Padova, Dipartimento di Matematica Pura e Applicata, Via Trieste 63, 35121 Padova, Italy, Italy |
2. | Space Research Institute, Profsoyuznaya 84/32, 117997 Moscow, Russian Federation |
[1] |
Sujit Nair, Naomi Ehrich Leonard. Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2007, 2 (4) : 597-626. doi: 10.3934/nhm.2007.2.597 |
[2] |
Sebastián Ferrer, Francisco J. Molero. Andoyer's variables and phases in the free rigid body. Journal of Geometric Mechanics, 2014, 6 (1) : 25-37. doi: 10.3934/jgm.2014.6.25 |
[3] |
Kai Koike. Wall effect on the motion of a rigid body immersed in a free molecular flow. Kinetic and Related Models, 2018, 11 (3) : 441-467. doi: 10.3934/krm.2018020 |
[4] |
Giancarlo Benettin, Anna Maria Cherubini, Francesco Fassò. Regular and chaotic motions of the fast rotating rigid body: a numerical study. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 521-540. doi: 10.3934/dcdsb.2002.2.521 |
[5] |
Arnab Roy, Takéo Takahashi. Local null controllability of a rigid body moving into a Boussinesq flow. Mathematical Control and Related Fields, 2019, 9 (4) : 793-836. doi: 10.3934/mcrf.2019050 |
[6] |
Meina Gao, Jianjun Liu. A degenerate KAM theorem for partial differential equations with periodic boundary conditions. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5911-5928. doi: 10.3934/dcds.2020252 |
[7] |
Kingshook Biswas. Complete conjugacy invariants of nonlinearizable holomorphic dynamics. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 847-856. doi: 10.3934/dcds.2010.26.847 |
[8] |
Banavara N. Shashikanth. Poisson brackets for the dynamically coupled system of a free boundary and a neutrally buoyant rigid body in a body-fixed frame. Journal of Geometric Mechanics, 2020, 12 (1) : 25-52. doi: 10.3934/jgm.2020003 |
[9] |
Joris Vankerschaver, Eva Kanso, Jerrold E. Marsden. The geometry and dynamics of interacting rigid bodies and point vortices. Journal of Geometric Mechanics, 2009, 1 (2) : 223-266. doi: 10.3934/jgm.2009.1.223 |
[10] |
Piotr Kokocki. Homotopy invariants methods in the global dynamics of strongly damped wave equation. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3227-3250. doi: 10.3934/dcds.2016.36.3227 |
[11] |
Matthias Hieber, Miho Murata. The $L^p$-approach to the fluid-rigid body interaction problem for compressible fluids. Evolution Equations and Control Theory, 2015, 4 (1) : 69-87. doi: 10.3934/eect.2015.4.69 |
[12] |
Paul Deuring, Stanislav Kračmar, Šárka Nečasová. A leading term for the velocity of stationary viscous incompressible flow around a rigid body performing a rotation and a translation. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1389-1409. doi: 10.3934/dcds.2017057 |
[13] |
Bernard Bonnard, Olivier Cots, Nataliya Shcherbakova. The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion. Mathematical Control and Related Fields, 2013, 3 (3) : 287-302. doi: 10.3934/mcrf.2013.3.287 |
[14] |
Šárka Nečasová, Joerg Wolf. On the existence of global strong solutions to the equations modeling a motion of a rigid body around a viscous fluid. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1539-1562. doi: 10.3934/dcds.2016.36.1539 |
[15] |
Brennan McCann, Morad Nazari. Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles. Journal of Geometric Mechanics, 2022, 14 (1) : 29-55. doi: 10.3934/jgm.2022002 |
[16] |
Yaobang Ye, Zongyu Zuo, Michael Basin. Robust adaptive sliding mode tracking control for a rigid body based on Lie subgroups of SO(3). Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1823-1837. doi: 10.3934/dcdss.2022010 |
[17] |
Xiaocai Wang, Junxiang Xu, Dongfeng Zhang. A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2141-2160. doi: 10.3934/dcds.2017092 |
[18] |
Zhichao Ma, Junxiang Xu. A KAM theorem for quasi-periodic non-twist mappings and its application. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 3169-3185. doi: 10.3934/dcds.2022013 |
[19] |
Martijn Bos, Silvio Traversaro, Daniele Pucci, Alessandro Saccon. Efficient geometric linearization of moving-base rigid robot dynamics. Journal of Geometric Mechanics, 2022 doi: 10.3934/jgm.2022009 |
[20] |
Davide L. Ferrario, Alessandro Portaluri. Dynamics of the the dihedral four-body problem. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 925-974. doi: 10.3934/dcdss.2013.6.925 |
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