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Mat. Sb., 1903, Volume 24, Number 1, Pages 139–168 (Mi msb6665)  

This article is cited in 44 scientific papers (total in 45 papers)

Sur le roulement d'une sphère sur un plan

S. A. Tchaplyguine


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Citation: S. A. Tchaplyguine, “Sur le roulement d'une sphère sur un plan”, Mat. Sb., 24:1 (1903), 139–168

Citation in format AMSBIB
\Bibitem{Tch03}
\by S.~A.~Tchaplyguine
\paper Sur le roulement d'une sph\`ere sur un plan
\jour Mat. Sb.
\yr 1903
\vol 24
\issue 1
\pages 139--168
\mathnet{http://mi.mathnet.ru/msb6665}
\zmath{https://zbmath.org/?q=an:34.0782.01}


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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. A. P. Veselov, L. E. Veselova, “Currents on Lie groups with nonholonomic connection and integrable nonhamiltonian systems”, Funct. Anal. Appl., 20:4 (1986), 308–309  mathnet  crossref  mathscinet  zmath  isi
    2. Borisov A., Tsygvintsev A., “Kovalevskaya's Method in Rigid Body Dynamics”, Pmm-J. Appl. Math. Mech., 61:1 (1997), 27–32  isi
    3. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Gamiltonizatsiya negolonomnykh sistem v okrestnosti invariantnykh mnogoobrazii”, Nelineinaya dinam., 6:4 (2010), 829–854  mathnet  elib
    4. Jovanovic B., “Hamiltonization and Integrability of the Chaplygin Sphere in R-N”, J. Nonlinear Sci., 20:5 (2010), 569–593  crossref  isi
    5. 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
    6. A. V. Tsyganov, “Deformatsii kanonicheskoi skobki Puassona dlya negolonomnykh sistem Chaplygina i Borisova–Mamaeva–Fëdorova pri nulevoi konstante ploschadei. I”, Nelineinaya dinam., 7:3 (2011), 577–599  mathnet
    7. A. V. Tsyganov, “O bigamiltonovoi strukture sistem Chaplygina i Borisova–Mamaeva–Fedorova pri nulevoi konstante ploschadei. II”, Nelineinaya dinam., 8:1 (2012), 43–55  mathnet
    8. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kak upravlyat sharom Chaplygina pri pomoschi rotorov”, Nelineinaya dinam., 8:2 (2012), 289–307  mathnet
    9. A. V. Tsyganov, “O puassonovykh strukturakh, voznikayuschikh pri rassmotrenii shara Chaplygina i ego obobschenii”, Nelineinaya dinam., 8:2 (2012), 345–353  mathnet
    10. A. V. Tsyganov, “O negolonomnykh sistemakh Veselovoi i Chaplygina”, Nelineinaya dinam., 8:3 (2012), 541–547  mathnet
    11. I. I. Ovsyannikov, “Ob ustoichivosti dvizheniya shara Chaplygina na ploskosti s proizvolnym zakonom treniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 140–145  mathnet
    12. A. V. Borisov, I. S. Mamaev, “Topologicheskii analiz odnoi integriruemoi sistemy, svyazannoi s kacheniem shara po sfere”, Nelineinaya dinam., 8:5 (2012), 957–975  mathnet
    13. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kak upravlyat sharom Chaplygina pri pomoschi rotorov. II”, Nelineinaya dinam., 9:1 (2013), 59–76  mathnet
    14. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    15. A. V. Tsyganov, “O share Chaplygina v absolyutnom prostranstve”, Nelineinaya dinam., 9:4 (2013), 711–719  mathnet
    16. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara Chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754  mathnet
    17. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The Problem of Drift and Recurrence for the Rolling Chaplygin Ball”, Regul. Chaotic Dyn., 18:6 (2013), 832–859  mathnet  crossref  mathscinet  zmath
    18. Mikhail Svinin, Akihiro Morinaga, Motoji Yamamoto, “On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors”, Regul. Chaotic Dyn., 18:1-2 (2013), 126–143  mathnet  crossref  mathscinet  zmath
    19. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “How to Control the Chaplygin Ball Using Rotors. II”, Regul. Chaotic Dyn., 18:1-2 (2013), 144–158  mathnet  crossref  mathscinet  zmath
    20. Peter Lynch, Miguel D. Bustamante, “Quaternion Solution for the Rocknroller: Box Orbits, Loop Orbits and Recession”, Regul. Chaotic Dyn., 18:1-2 (2013), 166–183  mathnet  crossref  mathscinet  zmath
    21. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328  mathnet  crossref  mathscinet  zmath
    22. Alexey V. Borisov, Ivan S. Mamaev, “Topological Analysis of an Integrable System Related to the Rolling of a Ball on a Sphere”, Regul. Chaotic Dyn., 18:4 (2013), 356–371  mathnet  crossref  mathscinet  zmath
    23. Stefan Rauch-Wojciechowski, Nils Rutstam, “Dynamics of the Tippe Top Properties of Numerical Solutions Versus the Dynamical Equations”, Regul. Chaotic Dyn., 18:4 (2013), 453–467  mathnet  crossref  mathscinet  zmath
    24. 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
    25. A. V. Borisov, A. O. Kazakov, I. R. Sataev, “Regulyarnye i khaoticheskie attraktory v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 10:3 (2014), 361–380  mathnet
    26. Andrey V. Tsiganov, “On the Lie Integrability Theorem for the Chaplygin Ball”, Regul. Chaotic Dyn., 19:2 (2014), 185–197  mathnet  crossref  mathscinet  zmath
    27. Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “The Reversal and Chaotic Attractor in the Nonholonomic Model of Chaplygins Top”, Regul. Chaotic Dyn., 19:6 (2014), 718–733  mathnet  crossref  mathscinet  zmath
    28. “Kommentarii nauchnogo redaktora”, Nelineinaya dinam., 11:2 (2015), 443–445  mathnet
    29. 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
    30. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “On the Hadamard–Hamel Problem and the Dynamics of Wheeled Vehicles”, Regul. Chaotic Dyn., 20:6 (2015), 752–766  mathnet  crossref  mathscinet  adsnasa
    31. I. R. Sataev, A. O. Kazakov, “Stsenarii perekhoda k khaosu v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 12:2 (2016), 235–250  mathnet  elib
    32. Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810  mathnet  crossref
    33. Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901  mathnet  crossref
    34. Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954  mathnet  crossref
    35. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Historical and critical review of the development of nonholonomic mechanics: the classical period”, Regular and Chaotic Dynamics, 21:4 (2016), 455–476  mathnet  crossref  crossref  zmath  elib
    36. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dynamics of the Chaplygin sleigh on a cylinder”, Regular and Chaotic Dynamics, 21:1 (2016), 136–146  mathnet  crossref  crossref  mathscinet  zmath  elib
    37. A. I. Zhila, “Chaplygin's ball with a rotor: Non-degeneracy of singular points”, Moscow University Mathematics Bulletin, 71:2 (2016), 45–54  mathnet  crossref  mathscinet  isi  elib
    38. Andrey V. Tsiganov, “Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball”, Regul. Chaotic Dyn., 22:4 (2017), 353–367  mathnet  crossref
    39. 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
    40. A. I. Zhila, “Comparison of the system “Chaplygin ball with a rotor” and the Zhukovskii system from the rough Liouville equivalence point of view”, Moscow University Mathematics Bulletin, 72:6 (2017), 245–250  mathnet  crossref  mathscinet  isi
    41. Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186  mathnet  crossref
    42. Alexander A. Kilin, Elena N. Pivovarova, “Qualitative Analysis of the Nonholonomic Rolling of a Rubber Wheel with Sharp Edges”, Regul. Chaotic Dyn., 24:2 (2019), 212–233  mathnet  crossref
    43. E. A. Mityushov, N. E. Misyura, S. A. Berestova, “Kvaternionnaya model programmnogo upravleniya dvizheniem shara Chaplygina”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 408–421  mathnet  crossref
    44. Kurt M. Ehlers, Jair Koiller, “Cartan meets Chaplygin”, Theor. Appl. Mech., 46:1 (2019), 15–46  mathnet  crossref
    45. Božidar Jovanović, “Note on a ball rolling over a sphere: integrable Chaplygin system with an invariant measure without Chaplygin Hamiltonization”, Theor. Appl. Mech., 46:1 (2019), 97–108  mathnet  crossref
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