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New case of complete integrability of dynamics equations on a tangent fibering to a 3D sphere

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Abstract

The paper presents the results of study of the motion equations for a dynamically symmetric 4D-rigid body placed in a certain non-conservative field of forces. The form of the field is taken from the dynamics of actual 2D- and 3D-rigid bodies interacting with the medium in the case when the system contains a non-conservative pair of forces forcing the center of mass of a body to move rectilinearly and uniformly. A new case of integrability is obtained for dynamic equations of body motion in a resisting medium filling a four-dimensional space under presence of a tracking force.

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References

  1. M. V. Shamolin, Methods of Analysis of Dynamic Systems with Variable Dissipation in Rigid Dynamics (Ekzamen, Moscow, 2007) [in Russian].

  2. M. V. Shamolin, “Jacobi Integrability in the Problem of Motion of a Four-Dimensional Rigid Body in a Resistant Medium,” Doklady Russ. Akad. Nauk 375 (3), 343 (2000).

    Google Scholar 

  3. M. V. Shamolin, “Integrability in Transcendental Functions,” Uspekhi Matem. Nauk 53 (3), 209 (1998).

    Article  MathSciNet  Google Scholar 

  4. O. I. Bogoyavlenskii, “Some Integrable Cases of Euler Equations,” Doklady Akad. Nauk SSSR 287 (5), 1105 (1986).

    MathSciNet  Google Scholar 

  5. O. I. Bogoyavlenskii, “Dynamics of a Rigid Body with n Ellipsoidal Cavities Filled with Magnetic Fluid,” Doklady Akad. Nauk SSSR 272 (6), 1364 (1983).

    MathSciNet  Google Scholar 

  6. A. P. Veselov, “Landau-Lifshits Equation and Integrable Systems of Classic Mechanics,” Doklady Akad. Nauk SSSR 270 (5), 1094 (1983).

    MathSciNet  MATH  Google Scholar 

  7. A. P. Veselov, “Conditions of Integrability of Euler Equations on so(4),” Doklady Akad. Nauk SSSR 270 (6), 1298 (1983).

    MathSciNet  Google Scholar 

  8. S. V. Manakov, “Remark on Integration of Euler Equations for Dynamics of an n-Dimensional Rigid Body,” Funkts. Anal. Prilozhen. 10 (4), 93 (1976).

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Research Institute of Mechanics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    M. V. Shamolin

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  1. M. V. Shamolin
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Correspondence to M. V. Shamolin.

Additional information

Original Russian Text © M.V. Shamolin, 2015, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2015, Vol. 70, No. 3, pp. 11–14.

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Shamolin, M.V. New case of complete integrability of dynamics equations on a tangent fibering to a 3D sphere. Moscow Univ. Math. Bull. 70, 111–114 (2015). https://doi.org/10.3103/S002713221503002X

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  • DOI: https://doi.org/10.3103/S002713221503002X

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