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Mat. Zametki, 1988, Volume 44, Issue 5, Pages 604–619 (Mi mz4214)  

This article is cited in 30 scientific papers (total in 30 papers)

Integrable nonholonomic systems on Lie groups

A. P. Veselov, L. E. Veselova

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English version:
Mathematical Notes, 1988, 44:5, 810–819

Bibliographic databases:

UDC: 517.9
Received: 05.05.1988

Citation: A. P. Veselov, L. E. Veselova, “Integrable nonholonomic systems on Lie groups”, Mat. Zametki, 44:5 (1988), 604–619; Math. Notes, 44:5 (1988), 810–819

Citation in format AMSBIB
\by A.~P.~Veselov, L.~E.~Veselova
\paper Integrable nonholonomic systems on Lie groups
\jour Mat. Zametki
\yr 1988
\vol 44
\issue 5
\pages 604--619
\jour Math. Notes
\yr 1988
\vol 44
\issue 5
\pages 810--819

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Fedorov, YN, “Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces”, Journal of Nonlinear Science, 14:4 (2004), 341  isi
    2. A. V. Borisov, I. S. Mamaev, “Isomorphism and Hamilton representation of some nonholonomic systems”, Siberian Math. J., 48:1 (2007), 26–36  mathnet  crossref  mathscinet  zmath  isi
    3. Garcia-Naranjo, L, “Reduction of almost Poisson brackets for nonholonomic systems on Lie groups”, Regular & Chaotic Dynamics, 12:4 (2007), 365  crossref  isi
    4. Koiller J., Ehlers K., “Rubber rolling over a sphere”, Regular & Chaotic Dynamics, 12:2 (2007), 127–152  crossref  isi
    5. Borisov, AV, “Conservation Laws, Hierarchy of Dynamics and Explicit Integration of Nonholonomic Systems”, Regular & Chaotic Dynamics, 13:5 (2008), 443  crossref  isi
    6. Borisov, AV, “Chaplygin ball over a fixed sphere: an explicit integration”, Regular & Chaotic Dynamics, 13:6 (2008), 557  crossref  isi
    7. Fedorov, YN, “Hamiltonization of the generalized Veselova LR system”, Regular & Chaotic Dynamics, 14:4–5 (2009), 495  crossref  isi
    8. Jovanovic, B, “LR and L plus R systems”, Journal of Physics A-Mathematical and Theoretical, 42:22 (2009), 225202  crossref  isi
    9. I. S. Mamaev, “Universalnyi kompleks programm dlya issledovaniya mekhanicheskikh sistem s negolonomnymi svyazyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 2, 147–160  mathnet
    10. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kachenie odnorodnogo shara po dinamicheski nesimmetrichnoi sfere”, Nelineinaya dinam., 6:4 (2010), 869–889  mathnet
    11. Jovanovic B., “Hamiltonization and Integrability of the Chaplygin Sphere in R-N”, J. Nonlinear Sci., 20:5 (2010), 569–593  crossref  isi
    12. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Obobschenie preobrazovaniya Chaplygina i yavnoe integrirovanie sharovogo podvesa”, Nelineinaya dinam., 7:2 (2011), 313–338  mathnet  elib
    13. A. V. Tsiganov, “One family of conformally Hamiltonian systems”, Theoret. and Math. Phys., 173:2 (2012), 1481–1497  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    14. A. V. Tsyganov, “O negolonomnykh sistemakh Veselovoi i Chaplygina”, Nelineinaya dinam., 8:3 (2012), 541–547  mathnet
    15. Tsiganov A.V., “On the Poisson Structures for the Nonholonomic Chaplygin and Veselova Problems”, Regul. Chaotic Dyn., 17:5 (2012), 439–450  crossref  isi
    16. Balseiro P. Garcia-Naranjo L.C., “Gauge Transformations, Twisted Poisson Brackets and Hamiltonization of Nonholonomic Systems”, Arch. Ration. Mech. Anal., 205:1 (2012), 267–310  crossref  isi
    17. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Geometrizatsiya teoremy Chaplygina o privodyaschem mnozhitele”, Nelineinaya dinam., 9:4 (2013), 627–640  mathnet
    18. Luis C. García-Naranjo, Juan C. Marrero, “Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane”, Regul. Chaotic Dyn., 18:4 (2013), 372–379  mathnet  crossref  mathscinet  zmath
    19. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. Bolsinov A.V. Borisov A.V. Mamaev I.S., “Geometrisation of Chaplygin'S Reducing Multiplier Theorem”, Nonlinearity, 28:7 (2015), 2307–2318  crossref  isi
    21. Guha P., “Nonholonomic Deformation of Coupled and Supersymmetric KdV Equations and Euler-Poincaré-Suslov Method”, Rev. Math. Phys., 27:4 (2015), 1550011  crossref  isi
    22. Božidar Jovanović, “Invariant Measures of Modified $\mathrm{LR}$ and $\mathrm{L+R}$ Systems”, Regul. Chaotic Dyn., 20:5 (2015), 542–552  mathnet  crossref  mathscinet  zmath
    23. A. V. Borisov, I. S. Mamaev, “Simmetrii i reduktsiya v negolonomnoi mekhanike”, Nelineinaya dinam., 11:4 (2015), 763–823  mathnet
    24. Alexey V. Borisov, Ivan S. Mamaev, “Symmetries and Reduction in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604  mathnet  crossref  mathscinet  zmath
    25. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. Jovanovic B., “Rolling Balls Over Spheres in R-N”, Nonlinearity, 31:9 (2018), 4006–4030  crossref  isi
    27. B. Gajić, B. Jovanović, “Two Integrable Cases of a Ball Rolling over a Sphere in $\mathbb{R}^n$”, Rus. J. Nonlin. Dyn., 15:4 (2019), 457–475  mathnet  crossref  elib
    28. Garcia-Naranjo L.C. Marrero J.C., “The Geometry of Nonholonomic Chaplygin Systems Revisited”, Nonlinearity, 33:3 (2020), 1297–1341  crossref  isi
    29. Vladimir Dragović, Borislav Gajić, Božidar Jovanović, “Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis”, Theor. Appl. Mech., 47:2 (2020), 257–287  mathnet  crossref
    30. Balseiro P. Yapu L.P., “Conserved Quantities and Hamiltonization of Nonholonomic Systems”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 38:1 (2021), 23–60  crossref  isi
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