Abstract:
The Hamiltonian representation and integrability of the nonholonomic Suslov problem and its generalization suggested by S. A. Chaplygin are considered. This subject is important for understanding the qualitative features of the dynamics of this system, being in particular related to a nontrivial asymptotic behavior (i. e., to a certain scattering problem). A general approach based on studying a hierarchy in the dynamical behavior of nonholonomic systems is developed.
Citation:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Hamiltonicity and integrability of the Suslov problem”, Regul. Chaotic Dyn., 16:1-2 (2011), 104–116
\Bibitem{BorKilMam11}
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper Hamiltonicity and integrability of the Suslov problem
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 1-2
\pages 104--116
\mathnet{http://mi.mathnet.ru/rcd430}
\crossref{https://doi.org/10.1134/S1560354711010035}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2774382}
\zmath{https://zbmath.org/?q=an:1277.70008}
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https://www.mathnet.ru/eng/rcd430
https://www.mathnet.ru/eng/rcd/v16/i1/p104
This publication is cited in the following 41 articles:
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E. A. Mikishanina, “Omnikolesnaya realizatsiya zadachi Suslova s reonomnoi svyazyu: dinamicheskaya model i upravlenie”, Vestnik rossiiskikh universitetov. Matematika, 29:147 (2024), 296–308
Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106
A. A. Kilin, T. B. Ivanova, “The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:1 (2023), 3–17
A. J. Maciejewski, M. Przybylska, “Gyrostatic Suslov Problem”, Rus. J. Nonlin. Dyn., 18:4 (2022), 609–627
E. A. Mikishanina, “Issledovanie vliyaniya sluchainykh vozmuschenii na dinamiku sistemy v zadache Suslova”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2021, no. 73, 17–29
Bizyaev I. Bolotin S. Mamaev I., “Normal Forms and Averaging in An Acceleration Problem in Nonholonomic Mechanics”, Chaos, 31:1 (2021), 013132
Alexey V. Borisov, Evgeniya A. Mikishanina, “Two Nonholonomic Chaotic Systems. Part I. On the Suslov Problem”, Regul. Chaotic Dyn., 25:3 (2020), 313–322
Bizyaev I.A. Mamaev I.S., “Dynamics of the Nonholonomic Suslov Problem Under Periodic Control: Unbounded Speedup and Strange Attractors”, J. Phys. A-Math. Theor., 53:18 (2020), 185701
Alexey Bolsinov, Jinrong Bao, “A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras”, Regul. Chaotic Dyn., 24:3 (2019), 266–280
Vyacheslav P. Kruglov, Sergey P. Kuznetsov, “Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators”, Regul. Chaotic Dyn., 24:6 (2019), 725–738
Borisov A.V. Kilin A.A. Pivovarova E.N., “Speedup of the Chaplygin TOP By Means of Rotors”, Dokl. Phys., 64:3 (2019), 120–124
Borisov A. Kilin A. Mamaev I., “Invariant Submanifolds of Genus 5 and a Cantor Staircase in the Nonholonomic Model of a Snakeboard”, Int. J. Bifurcation Chaos, 29:3 (2019), 1930008
Shengda Hu, Manuele Santoprete, “Suslov Problem with the Clebsch–Tisserand Potential”, Regul. Chaotic Dyn., 23:2 (2018), 193–211
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane”, Regul. Chaotic Dyn., 23:6 (2018), 665–684
Alexander A. Kilin, Elena N. Pivovarova, “Integrable Nonsmooth Nonholonomic Dynamics of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 23:7-8 (2018), 887–907
Putkaradze V., Rogers S., “Constraint Control of Nonholonomic Mechanical Systems”, J. Nonlinear Sci., 28:1 (2018), 193–234
A. V. Borisov, I. S. Mamaev, “Neodnorodnye sani Chaplygina”, Nelineinaya dinam., 13:4 (2017), 625–639
A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
Alexey V. Borisov, Ivan S. Mamaev, “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447
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