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Cases of Integrability of Three-Dimensional Dynamic Equations for a Solid

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Abstract

A dynamic model of the interaction of a rigid body with a jet flow of a resistant medium is considered. This model allows us to obtain three-dimensional analogs of plane dynamic solutions for a solid interacting with the medium and to reveal new cases where the equations are Jacobi integrable. In such cases, the integrals are expressed in terms of elementary functions. The classical problems of a spherical pendulum in a flow and three-dimensional motion of a body with a servoconstraint are shown to be integrable. Mechanical and topological analogs of these problems are found

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REFERENCES

  1. M. I. Gurevich, The Theory of Jets of a Perfect Fluid [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  2. B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, Introduction to the Problem of a Body Moving in a Resistant Medium [in Russian], Izd. MGU, Moscow (1986).

    Google Scholar 

  3. V. A. Samsonov and M. V. Shamolin, “The problem of a body moving in a resistant medium, revisited,” Vestn. MGU, Ser. 1, Mat. Mekh., No. 3, 51–54 (1989).

  4. V. A. Samsonov and M. V. Shamolin, A Model Problem of a Moving Body in a Jet Flow [in Russian], Report No. 3969, Inst. Mekh., Izd. MGU, Moscow (1990).

    Google Scholar 

  5. S. A. Chaplygin, Selected Works [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  6. M. V. Shamolin, “A new two-parameter family of phase-plane portraits in the problem of a body moving in a medium,” Dokl. RAN, 337, No. 5, 611–614 (1994).

    Google Scholar 

  7. M. V. Shamolin, “Variety of phase-plane portraits in the dynamics of a solid interacting with a resistant medium,” Dokl. RAN, 349, No. 2, 193–197 (1996).

    Google Scholar 

  8. M. V. Shamolin, “A list of integrals of the dynamic equations in the three-dimensional problem of a body moving in a resistant medium,” in: Abstracts of Papers Read at Sci. Conf. on Modeling and Stability Analysis of Systems (May 20-24, 1996) [in Russian], Kiev (1996).

  9. M. V. Shamolin, “On one integrable case in the three-dimensional dynamics of a body moving in a resistant medium,” in: Abstracts of Papers Read at the 2nd Symp. on Classical and Celestial Mechanics (Velikie Luki, August 23-28, 1996) [in Russian], Moscow- Velikie Luki (1996), pp. 91–92.

    Google Scholar 

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  1. Institute of Mechanics of the, Moscow State University, Moscow, Russia

    M. V. Shamolin

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  1. M. V. Shamolin
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Shamolin, M.V. Cases of Integrability of Three-Dimensional Dynamic Equations for a Solid. International Applied Mechanics 37, 769–777 (2001). https://doi.org/10.1023/A:1012411207560

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