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In the proposed cycle of work, we study the equations of the motion of dynamically symmetric fixed n-dimensional rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of the motion of a free n-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. In this work, we study the case of independence of force fields on the tensor of angular velocity.

About the authors

M. V. Shamolin

Institute of Mechanics, Lomonosov Moscow State University

Author for correspondence.
Email: morenov.sv@ssau.ru
Russian Federation


  1. Shamolin M.V. Sluchai integriruemosti, sootvetstvuiushchie dvizheniiu maiatnika na ploskosti . Vestnik SamGU. Estestvennonauchnaia seriia , 2015, no. 10(132), pp. 91–113 .
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  4. Pokhodnya N.V., Shamolin M.V. Nekotorye usloviia integriruemosti dinamicheskikh sistem v transtsendentnykh funktsiiakh . Vestnik SamGU. Estestvennonauchnaia seriia , 2013, no. 9/1(110), pp. 35–41 .
  5. Shamolin M.V. Novye sluchai integriruemykh sistem s dissipatsiei na kasatel’nom rassloenii trekhmernogo mnogoobraziia . Doklady RAN , 2017, Vol. 477, no. 2, pp. 168–172 .
  6. Shamolin M.V. Polnyi spisok pervykh integralov dinamicheskikh uravnenii dvizheniia mnogomernogo tverdogo tela v nekonservativnom pole , 2015, Vol. 461, no. 5, pp. 533–536 .
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  9. Trofimov V.V., Shamolin M.V. Geometricheskie i dinamicheskie invarianty integriruemykh gamil’tonovykh i dissipativnykh sistem . Fund. i prikl. mat. , 2010, Vol. 16, no. 4, pp. 3–229 .
  10. Shamolin M.V. Metody analiza dinamicheskikh sistem s peremennoi dissipatsiei v dinamike tverdogo tela . M.: Izd-vo ”Ekzamen ”, 2007, 352 p. .
  11. Shamolin M.V. Nekotorye model’nye zadachi dinamiki tverdogo tela pri vzaimodeistvii ego so sredoi . Prikl. mekhanika , 2007, Vol. 43, no. 10, pp. 49–67 .
  12. Shamolin M.V. Novye sluchai integriruemosti sistem s dissipatsiei na kasatel’nykh rassloeniiakh k dvumernoi i trekhmernoi sferam . Doklady RAN , 2016, Vol. 471, no. 5, pp. 547–551 .
  13. Shamolin M.V. Novye sluchai integriruemykh sistem s dissipatsiei na kasatel’nom rassloenii k mnogomernoi sfere . Doklady RAN , 2017, Vol. 474, no. 2, pp. 177–181 .
  14. Shamolin M.V. Novye sluchai integriruemykh sistem s dissipatsiei na kasatel’nom rassloenii dvumernogo mnogoobraziia . Doklady RAN , 2017, Vol. 475, no. 5, pp. 519–523 .

Copyright (c) 2018 М. В. Шамолин

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