Peculiarities of Statics and Dynamics of the Heavy Ellipsoid on the Rough Inclined Plane

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Abstract

The problems of equilibria and steady rotations of the heavy body-ellipsoid on the rough inclined plane are considered in this paper. The body makes point contact with this plane without slippage (nonholonomic constraint). All positions of equilibria of the ellipsoid are found. In this paper is shown that all these positions are not stable in the spatial case when perturbations of the body can occur with spinning. Besides, as is shown in this paper, steady rotations of the heavy body-ellipsoid on the rough inclined plane cannot be realized.

About the authors

G. M. Rozenblat

Moscow Automobile and Road Construction State Technical University (MADI)

Author for correspondence.
Email: gr51@mail.ru
Russia, Moscow

References

  1. Markeev A.P. On nonlinear oscillations of a triaxial ellipsoid on a smooth horizontal plane // PMM, 2022, vol. 86, no. 6, pp. 784–800. (in Russian)
  2. Markeev A.P. Dynamics of a Body in Contact with a Solid Surface. Moscow; Izhevsk: Inst. Comput. Res.; Nauka, 2014. 496 p. (in Russian)
  3. Zhuralev V.Ph. Ill-posed problems in mechanics // Mech. Solids, 2016, vol. 51, no. 5, pp. 538–541.
  4. Zhuralev V.Ph., Rozenblat G.M. Paradoxes, Counterexamples and Mistakes in Mechanics. Moscow: Lenand, 2017. 240 p. (in Russian)
  5. Delone N.B. Cours of Theoretical Mechanics for Technicians and Engineers. Moscow: Lenand, 2021. 432 p. (in Russian)
  6. Ivanov A.P. The stability of equilibrium in systems with friction // JAMM, 2007, vol. 71, iss. 3, pp. 385–395.
  7. Zhuralev V.F., Rozenblat G.M. Theoretical Mechanics in Decisions of Problems from Book by I.V. Meschersky: Systems with Rolling. Nonholonomic Constraints. Moscow: Librokom, 2013. 192 p. (in Russian)
  8. Rubanovsky V.N., Samsonov V.A. Stability of Steady Rotations in Examples and Problems. Moscow: Nauka, 1988. 304 p. (in Russian)
  9. Bizyaev I.A., Mamaev I.S. Permanent rotations in nonholonomic mechanics. omnirotational ellipsoid // R&C Dyn., 2022, vol. 27, no. 6, pp. 587–612.
  10. Karapetyan A.V. Stability of the Permanent Rotations. М.: “Editorial URSS”, 1998. 168 p. (in Russian)
  11. Karapetyan A.V. Stability and Bifurcation of the Motion. Moscow: MSU Publ., 2020. 186 с. (in Russian)

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