ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

vol 63 / December, 2020

DOI 10.17586/0021-3454-2018-61-2-129-134

UDC 531.47+531.536+531.555.1


V. V. Chistov
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University), Saint Petersburg, Russia; student

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Abstract. The dynamics of free and forced rotation of a rigid body around the central but not the principal axis of inertia Oz, supported by a bearing and thrust bearing, is modeled mechanically under the conditions of hydrodynamic and dry friction. It is shown that The inertial pairs and pairs of dry friction arising in the plane of the axis are shown to depend not only on the centrifugal moments of inertia and the angular velocity, but also on the acceleration. The revealed dependence leads to dynamic equations with an irrational right-hand side in the general case, and with a discontinuous one in the particular case. The equations for simplest types of the motion are integrated analytically and numerically.
Keywords: dynamic disbalance, rotator, D'Alembert's principle, inertial pairs, bearing, thrust bearing, dry friction, hydrodynamic resistance, kinetics

  1. Appell P. Traité de mécanique rationnelle. Tome 2. Dynamique des systéms mécanique analytique, Paris, Gauthier-Villars, Éditeur, 1953, 487 p.
  2. Lur'e A.I. Analiticheskaya mekhanika (Analytical Mechanics), Moscow, 1961. (in Russ.)
  3. Smirnov Yu.P. Sbornik nauchno-metodicheskikh statey po teoreticheskoy mekhanike (Collection of Scientific and Methodological Articles on Theoretical Mechanics), Moscow, 1981, no. 11, pp. 184. (in Russ.)
  4. Polunin A.I.J. of Pharmacy and Technology, 2016, no. 4(8), December, pp.22726–22742.
  5. Bulsara M. et al. J. of Engineering Design and Technology, 2016, no. 2(14), pp. 277–285. 
  6. Chistyakov V.V. Applied nonlinear dynamics. Higher education Bulletin, 2014, no. 2(22), pp. 3–15. (in Russ.)
  7. Chistyakov V.V. Bulletin of Udmurt State University. Series Mathematics. Mechanics. Computer science, 2014, no. 2, pp. 153–163. (in Russ.)
  8. Borisov A.V., Jalnin A.Yu., Kuznetsov S.P. et al. Regular and Chaotic Dynamics, 2012, no. 6(17), pp. 512–526.
  9. Kondo Y., Nakanishi H. Phys. Rev. E, 2017, no. 6(95), April. DOI: 10.1103/PhysRevE.95.062207.
  10. Nanda A., Singla P., Amin Karami M. J. of Sound and Vibration, 2015, no. 369, December. DOI: 10.1016/j.jsv.2015.12.032.
  11. Markeev A.P. Teoreticheskaya mekhanika (Theoretical Mechanics), Moscow, 1999, 412 р. (in Russ.)
  12. Reshetov D.N. Detali mashin (Details of Machines), Moscow, 1989, 496 р. (in Russ.)
  13. Painlev´e P. Lecons sur le frottement, Paris, Hermann, 1895.