Doklady Physics

, Volume 61, Issue 9, pp 476–480 | Cite as

A multidimensional pendulum in a nonconservative force field under the presence of linear damping

Mechanics
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Abstract

A nonconservative force field in the dynamics of a multidimensional solid is constructed according to the results from the dynamics of real solids occurring in the force field of the action of the medium. In this case, it becomes possible to generalize the equations of motion of a multidimensional solid in a similarly constructed field of forces and to obtain a complete list of, generally speaking, transcendental first integrals expressed through a finite combination of elementary functions. In the study, the integrability in elementary functions is shown for the simultaneous equations of motion of a dynamically symmetric fixed multidimensional solid under the action of a nonconservative pair of forces in the presence of the linear damping moment (the additional dependence of the force field on the tensor of angular velocity of the solid).

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References

  1. 1.
    S. V. Manakov, Funktsion. Analiz Prilozh. 10 (4), 93 (1976).MathSciNetGoogle Scholar
  2. 2.
    A. P. Veselov, Dokl. Akad. Nauk 270 (6), 1298 (1983).MathSciNetGoogle Scholar
  3. 3.
    O. I. Bogoyavlenskii, Dokl. Akad. Nauk 287 (5), 1105 (1986).ADSMathSciNetGoogle Scholar
  4. 4.
    V. A. Samsonov and M. V. Shamolin, Vestn. Mosk. Univ. Ser. Mat. Mekh., No. 3, 51 (1989).MathSciNetGoogle Scholar
  5. 5.
    M. V. Shamolin, Method of Analysis of Dynamic Sets with Variable Dissipation in Dynamics of Solid (Ekzamen, Moscow, 2007) [in Russian].Google Scholar
  6. 6.
    M. V. Shamolin, in: Results of Science and Technics (VINITI, Moscow, 2013), Vol. 125, pp. 5–254 [in Russian].Google Scholar
  7. 7.
    M. V. Shamolin, Dokl. Phys. 44 (2), 110 (1999).ADSMathSciNetGoogle Scholar
  8. 8.
    M. V. Shamolin, Dokl. Phys. 57 (2), 78 (2012).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    M. V. Shamolin, Dokl. Phys. 57 (6), 250 (2012).ADSCrossRefGoogle Scholar
  10. 10.
    M. V. Shamolin, Dokl. Phys. 45 (11), 632 (2000).ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    M. V. Shamolin, Dokl. Phys. 54 (3), 155 (2009).ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    M. V. Shamolin, Dokl. Phys. 58 (1), 496 (2013).ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    S. A. Chaplygin, Compl. Colectl. of Works (Izd-vo AN SSSR, Leningrad, 1933), Vol. 1, pp. 133–135 [in Russian].Google Scholar
  14. 14.
    M. V. Shamolin, Usp. Mat. Nauk 53 (3), 209 (1998).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Research Institute of MechanicsMoscow State UniversityMoscowRussia

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