Speedup of a Chaplygin top by means of rotors

Cover Page

Cite item

Full Text

Abstract

In this paper we consider the control of the motion of a dynamically asymmetric unbalanced ball (Chaplygin top) by means of two perpendicular rotors. We propose a mechanism for control by periodically changing the gyrostatic momentum of the system, which leads to an unbounded speedup. We then formulate a general hypothesis of the mechanism for speeding up spherical bodies on a plane by periodically changing the system parameters.

About the authors

A. V. Borisov

Udmurt State University; Research Robotics Development Center Innopolis University

Email: archive@rcd.ru
Russian Federation, 1, Universitetskaya street, Izhevsk, 426034; 1, Universitetskaya street, Innopolis, 420500

A. A. Kilin

Udmurt State University; Moscow Institute of Physics and Technology

Email: archive@rcd.ru
Russian Federation, 1, Universitetskaya street, Izhevsk, 426034; 9, Institutskij, Dolgoprudny, Moscow region, 141701

E. N. Pivovarova

Research Robotics Development Center Innopolis University; Moscow Institute of Physics and Technology

Author for correspondence.
Email: archive@rcd.ru
Russian Federation, 1, Universitetskaya street, Innopolis, 420500; 9, Institutskij, Dolgoprudny, Moscow region, 141701

References

  1. Bizyaev I. A., Borisov A. V., Kozlov V. V., Mamaev I. S. Fermi-Like Acceleration and Power-Law Energy Growth in Nonholonomic Systems // Nonlinearity. In press.
  2. Bizyaev I. A., Borisov A. V., Kuznetsov S. P. Chaplygin Sleigh with Periodically Oscillating Internal Mass // EPL. 2017. V. 119. № 6. 60008. 7 p.
  3. Bizyaev I. A., Borisov A. V., Mamaev I. S. The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration // Regul. Chaotic Dyn. 2017. V. 22. № 8. Р. 955-975.
  4. Borisov A. V., Mamaev I. S., Bizyaev I. A. The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere // Regul. Chaotic Dyn. 2013. V. 18. № 3. Р. 277-328.
  5. Cendra H., Etchechoury M. Rolling of a Symmetric Sphere on a Horizontal Plane without Sliding or Slipping // Rept. Math. Phys. 2006. V. 57. № 3. Р. 367-374.
  6. Ehlers K. M., Koiller J. Rubber Rolling: Geometry and Dynamics of 2-3-5 Distributions. In: Proc. IUTAM Symp. 2006 on Hamiltonian Dynamics, Vortex Structures, Turbulence. Moscow, 25-30 August 2006. М., 2006. P. 469-480.
  7. Koiller J., Ehlers K. M. Rubber Rolling over a Sphere // Regul. Chaotic Dyn. 2007. V. 12. № 2. Р. 127-152.
  8. Борисов А. В., Мамаев И. С. Динамика твердого тела. Гамильтоновы методы, интегрируемость, хаос. Ижевск: НИЦ “РХД” / Ин-т компьют. исслед., 2005.
  9. Bolotin S., Treschev D. Unbounded Growth of Energy in Nonautonomous Hamiltonian Systems // Nonlinearity. 1999. V. 12. P. 365-388.
  10. Gelfreich V., Rom-Kedar V., Turaev D. Fermi Acceleration and Adiabatic Invariants for Non-Autonomous Billiards // Chaos. 2012. V. 22. 033116.
  11. Lenz F., Diakonos F. K., Schmelcher P. Tunable Fermi Acceleration in the Driven Elliptical Billiard // Phys. Rev. Lett. 2008. V. 100. 014103.
  12. Pereira T., Turaev D. Exponential Energy Growth in Adiabatically Changing Hamiltonian Systems // Phys. Rev. E. 2015. V. 91. 010901.
  13. Borisov A. V., Mamaev I. S. Isomorphism and Hamilton Representation of Some Nonholonomic Systems // Sib. Math. J. 2007. V. 48. № 1. Р. 26-36.
  14. Borisov A. V., Kilin A. A., Mamaev I. S. Hamiltonicity and Integrability of the Suslov Problem // Regul. Chaotic Dyn. 2011. V. 16. № 1/2. Р. 104-116.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2019 Russian academy of sciences