Skip to main content
SpringerLink
Log in

Properties of Solutions to Gas Dynamics Equations on a Rotating Plane: the Case of Motions with Uniform Deformation

  • Published:
Moscow University Mechanics Bulletin Aims and scope

Abstract

A system of ideal polytropic gas equations written in the Lagrangian coordinates is considered on a uniformly rotating plane. For this system the first integrals corresponding to motions with uniform deformation are found. It is shown that, if the adiabatic index is equal to two, the original system consisting of four second-order nonlinear ordinary differential equations can be reduced to a single first-order equation and the solution can be found as a time function. The behavior of this solution is analyzed near equilibrium positions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. I. Sedov, Similarity and Dimensional Methods in Mechanics (Nauka, Moscow, 1972; CRC Press, Boca Raton, 1993).

    MATH  Google Scholar 

  2. O. S. Rozanova and M. K. Turzynski, “On Systems of Nonlinear ODE Arising in Gas Dynamics: Application to Vortical Motion,” in Differential and Difference Equations with Applications (Springer, Cham, 2018), Vol. 230, pp. 387–398.

    Chapter  Google Scholar 

  3. O. S. Rozanova and M. K. Turzynsky, “Nonlinear Stability of Localized and Non-localized Vortices in Rotating Compressible Media,” in Theory, Numerics and Applications of Hyperbolic Problems (Springer, Cham, 2018), Vol. 237, pp. 549–561.

    MATH  Google Scholar 

  4. L. V. Ovsyannikov, “A New Solution of the Equations of Hydrodynamics,” Dokl. Akad. Nauk SSSR 111 (1), 47–40 (1956).

    MathSciNet  MATH  Google Scholar 

  5. A. V. Borisov, I. S. Mamaev, and A. A. Kilin, “The Hamiltonian Dynamics of Self-Gravitating Liquid and Gas Ellipsoids,” Nelin. Dinam. 4 (4), 363–407 (2008).

    Article  Google Scholar 

  6. S. I. Anisimov and Yu. I. Lysikov, “Expansion of a Gas Cloud in Vacuum,” Prikl. Mat. Mekh. 34 (5), 926–929 (1970) [J. Appl. Math. Mech. 34 (5), 882–885 (1970)].

    MATH  Google Scholar 

  7. O. I. Bogoyavlensky, Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics (Nauka, Moscow, 1980; Springer, Berlin, 2011).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, 119899, Russia

    M. K. Turtsynskii

Authors
  1. M. K. Turtsynskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. K. Turtsynskii.

Additional information

Russian Text © The Author(s), 2020, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2020, Vol. 75, No. 2, pp. 39–46.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Turtsynskii, M.K. Properties of Solutions to Gas Dynamics Equations on a Rotating Plane: the Case of Motions with Uniform Deformation. Moscow Univ. Mech. Bull. 75, 37–43 (2020). https://doi.org/10.3103/S002713302002003X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S002713302002003X

Search

Navigation