On the stationary motions of a rigid body with a spherical support

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We conduct the qualitative analysis of differential equations describing the rotation of a dynamically asymmetric rigid body around a fixed point. The body is enclosed in a spherical shell, to which one ball and one disk adjoin. The motion of the body by inertia and under the action of potential forces is considered. It is established that in the absence of external forces, the differential equations have the families of solutions corresponding to the equilibrium positions of the body, and in the case of potential forces there exist manifolds of pendulum motions. For a number of the solutions, the necessary and sufficient conditions of the Lyapunov stability are derived.

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Sobre autores

V. Irtegov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences

Autor responsável pela correspondência
Email: irteg@icc.ru
Rússia, Irkutsk

T. Titorenko

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences

Email: titor@icc.ru
Rússia, Irkutsk

Bibliografia

  1. Chaplygin S.A. Rolling of a ball on a horizontal plane. Mat. Sb. 1903. V. 24. № 1. P. 139–168. (in Russian)
  2. Veselov A.P., Veselova L.E. Integrable nonholonomic systems on Lie groups // Math. Notes. 1988. V. 44. № 5. P. 810–819. https://doi.org/10.1007/BF01158420
  3. Borisov A.V., Mamaev I.S. A new integrable system of nonholonomic mechanics // Doklady Physics. 2015. V. 60. № 6. P. 269–271. https://doi.org/10.1134/S1028335815060087
  4. Crossley V.A. A Literature review on the design of spherical rolling robots. placeCityPittsburgh, StatePA, 2006. 6 p.
  5. Zhan Q. Motion planning of a spherical mobile robot // In: Motion and operation planning of robotic systems. Mechanisms and Machine Science. G. Carbone, F. Gomez-Bravo (eds.). Springer, 2015. V. 29. P. 361–381. https://doi.org/10.1007/978-3-319-14705-5_12
  6. Chi X., Zhan Q. Design and Modelling of an Amphibious Spherical Robot Attached with Assistant Fins // Appl. Sci. 2021. V. 11. № 9. 19 p. https://doi.org/10.3390/app11093739
  7. Poincare H. Memoire sur les courbes definies par une equation differentielle // Journal de Mathematiques Pures et Appliquees. 1881. V. 7. P. 375–422.
  8. Routh E.J. The advanced part of a treatise on the dynamics of a system of rigid bodies. 6 Edition. London: MacMillan and Co., 1905.
  9. Lyapunov A.M. On Permanent helical motions of a rigid body in fluid. Collected Works, USSR Acad. Sci. Moscow–Leningrad. 1954. V. 1. P. 276–319. (in Russian)
  10. Salvadori L. Sulla stabilita del movimento // Matematiche. 1969. V. 24. P. 218–238.
  11. Rumianstev V.V. On stability of motion of nonholonomic systems // Appl. Math. Mech. 1967. V. 31. Issue. 2. P. 282–293.
  12. Irtegov V.D. Invariant manifolds of stationary motions and their stability. Novosibirsk: Nauka, 1985. (in Russian)
  13. Bogoyavlenskii O.I. Two integrable cases of a rigid body dynamics in a force field // USSR Acad. Sci. Doklady. 1984. V. 275. № 6. P. 1359–1363. (in Russian)
  14. Borisov A.V., Mamaev I.S. Rigid body dynamics. Hamiltonian methods, Integrability, chaos. Moscow–Izhevsk: Institute of Computer Science, 2005. (in Russian)
  15. Irtegov V.D., Titorenko T.N. The invariant manifolds of systems with first integrals // Appl. Math. Mech. 2009. V. 73. Issue 4. P. 385–394. https://doi.org/10.1016/j.jappmathmech.2009.08.014

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