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Regular and Chaotic Dynamics
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Regular and Chaotic Dynamics, 2002, том 7, выпуск 2, страницы 201–219
DOI: https://doi.org/10.1070/RD2002v007n02ABEH000205 (Mi rcd812) 		 
Эта публикация цитируется в 102 научных статьях (всего в 103 статьях)

Nonholonomic Systems

The rolling motion of a ball on a surface. New integrals and hierarchy of dynamics

A. V. Borisova, I. S. Mamaevb, A. A. Kilinb

a Department of Theoretical Mechanic, Moscow State University, Vorob'ievy Gory, 119899, Moscow, Russia
b Laboratory of Dynamical Chaos and Nonlinearity, Udmurt State University, Universitetskaya, 1, 426034, Izhevsk, Russia
Список цитирования (103)
DOI: https://doi.org/10.1070/RD2002v007n02ABEH000205
Аннотация: The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also indicates a special case when an additional integral and invariant measure exist. Using this case, we obtain a nonholonomic generalization of the Jacobi problem for the inertial motion of a point on an ellipsoid. For a ball rolling, it is also shown that on an arbitrary cylinder in the gravity field the ball's motion is bounded and, on the average, it does not move downwards. All the results of the paper considerably expand the results obtained by E. Routh in XIX century.
Поступила в редакцию: 10.02.2002
Реферативные базы данных:
Тип публикации: Статья
MSC: 37J60, 37J55
Язык публикации: английский
Образец цитирования: A. V. Borisov, I. S. Mamaev, A. A. Kilin, “The rolling motion of a ball on a surface. New integrals and hierarchy of dynamics”, Regul. Chaotic Dyn., 7:2 (2002), 201–219
Цитирование в формате AMSBIB
\RBibitem{BorMamKil02}
\by A. V. Borisov, I. S. Mamaev, A. A. Kilin
\paper The rolling motion of a ball on a surface. New integrals and hierarchy of dynamics
\jour Regul. Chaotic Dyn.
\yr 2002
\vol 7
\issue 2
\pages 201--219
\mathnet{http://mi.mathnet.ru/rcd812}
\crossref{https://doi.org/10.1070/RD2002v007n02ABEH000205}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1912984}
\zmath{https://zbmath.org/?q=an:1058.70010}
Образцы ссылок на эту страницу:
  • https://www.mathnet.ru/rus/rcd812
  • https://www.mathnet.ru/rus/rcd/v7/i2/p201
    • Эта публикация цитируется в следующих 103 статьяx:
    1. Mariana Costa-Villegas, Luis C. García-Naranjo, “Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane”, Regul. Chaot. Dyn., 2025  crossref
    2. Paula Balseiro, Danilo Machado-Tereza, “Nonholonomic momentum map reduction and a Chaplygin-type foliation”, Nonlinearity, 38:5 (2025), 055006  crossref
    3. Alexander A. Kilin, Elena N. Pivovarova, “Bifurcation analysis of the problem of a “rubber” ellipsoid of revolution rolling on a plane”, Nonlinear Dyn, 2024  crossref
    4. Jin Yu, Wei Zhang, Rediet Tesfaye Zeru, Yuxi Xiao, Senchun Chai, “Dynamic Modeling Method for Constrained System with Singular Mass Matrices”, Applied Mathematical Modelling, 2024, 115780  crossref
    5. Alexander A. Kilin, Elena N. Pivovarova, Tatiana B. Ivanova, “Rolling of a Homogeneous Ball on a Moving Cylinder”, Regul. Chaot. Dyn., 2024  crossref
    6. Hiroshi Takano, “Analyzing the Motion of a Washer on a Rod”, Regul. Chaotic Dyn., 28:2 (2023), 227–250  mathnet  crossref  mathscinet
    7. Jiří Náprstek, Cyril Fischer, Vibration Control of Structures, 2023  crossref
    8. Francesco Fassò, Nicola Sansonetto, “On Some Aspects of the Dynamics of a Ball in a Rotating Surface of Revolution and of the Kasamawashi Art”, Regul. Chaotic Dyn., 27:4 (2022), 409–423  mathnet  crossref  mathscinet
    9. Aleksandar Obradović, Zoran Mitrović, Slaviša Šalinić, “On the problem of a heavy homogeneous ball rolling without slipping over a fixed surface of revolution”, Applied Mathematics and Computation, 420 (2022), 126906  crossref
    10. Marco Dalla Via, Francesco Fassò, Nicola Sansonetto, “On the Dynamics of a Heavy Symmetric Ball that Rolls Without Sliding on a Uniformly Rotating Surface of Revolution”, J Nonlinear Sci, 32:6 (2022)  crossref
    11. С. В. Соколов, “Памяти Алексея Владимировича Борисова”, Компьютерные исследования и моделирование, 13:1 (2021), 9–14  mathnet  crossref
    12. Christopher Cox, Renato Feres, Bowei Zhao, “Rolling Systems and Their Billiard Limits”, Regul. Chaotic Dyn., 26:1 (2021), 1–21  mathnet  crossref  mathscinet
    13. Naprstek J., Fischer C., “Trajectories of a Ball Moving Inside a Spherical Cavity Using First Integrals of the Governing Nonlinear System”, Nonlinear Dyn., 106:3 (2021), 1591–1625  crossref  isi  scopus
    14. Antali M., Havas V., Hogan S.J., Stepan G., “Nonlinear Dynamics of a Basketball Rolling Around the Rim”, Nonlinear Dyn., 104:4 (2021), 3013–3037  crossref  isi  scopus
    15. 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  mathscinet  isi  scopus
    16. Sabet S., Poursina M., Nikravesh P.E., “Control of Spherical Robots on Uneven Terrains”, 2021 IEEE/Rsj International Conference on Intelligent Robots and Systems (Iros), IEEE International Conference on Intelligent Robots and Systems, IEEE, 2021, 8159–8165  crossref  isi  scopus
    17. Ivanova T.B., “Non-Holonomic Rolling of a Ball on the Surface of a Rotating Cylinder”, ZAMM-Z. Angew. Math. Mech., 100:12 (2020), e202000067  crossref  mathscinet  isi  scopus
    18. Martins Flavius Portella Ribas, Fleury Agenor de Toledo, Trigo F.C., “Motion of a Disk in Contact With a Parametric 2D Curve and Painleve'S Paradox”, Multibody Syst. Dyn., 48:4 (2020), 427–450  crossref  mathscinet  zmath  isi  scopus
    19. Borisov A.V., Ivanova T.B., Kilin A.A., Mamaev I.S., “Circular Orbits of a Ball on a Rotating Conical Turntable”, Acta Mech., 231:3 (2020), 1021–1028  crossref  mathscinet  zmath  isi  scopus
    20. Chumley T., Cook S., Cox Ch., Feres R., “Rolling and No-Slip Bouncing in Cylinders”, J. Geom. Mech., 12:1 (2020), 53–84  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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