Skip to main content
SpringerLink
Log in

Virial oscillations of celestial bodies III. The solution of the evolutionary problem in non-newtonian time scale

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

Generalized Jacobi's equation is derived by introducing the friction force into the equations of motion of mass points constituting the system.

The exact solution of the equation of virial oscillations of celestial bodies written for non-conservative systems is obtained using non-linear time scale in the course of the change of variables for a particular friction force law.

The nature of the undamped virial oscillations of celestial bodies is though to be related to the system unstability near the state determined by the virial theorem. Thus, the friction force changes its sign near the unstable equilibrium state and due to dissipation of energy during evolution of the system the undamped virial oscillations can be described as self-exited oscillations.

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

  • Bogolubov, N. N. and Mitropolsky, Yu. A.: 1974,Asymptotic Methods in the Theory of Nonlinear Oscillations, Nauka, Moscow.

    Google Scholar 

  • Lightman, A. P. and Shapiro, S. L.: 1978,Rev. Mod. Phys. 50, 437.

    Google Scholar 

  • Ferronsky, V. I., Denisik, S. A., and Ferronsky, S. V.: 1978,Celest. Mech. 18, 113.

    Google Scholar 

  • Ferronsky, V. I., Denisik, S. A., and Ferronsky, S. V.: 1979,Celest. Mech. 20, 143.

    Google Scholar 

  • Ferronsky, V. I., Denisik, S. A., and Ferronsky, S. V.: 1981,Celest. Mech. 23, 243.

    Google Scholar 

  • Ferronsky, V. I., Denisik, S. A., and Ferronsky, S. V.: 1982,Celest. Mech. 27, 285.

    Google Scholar 

  • Ferronsky, V. I., Denisik, S. A., and Ferronsky, S. V.: 1984,Celest. Mech. (in press).

Download references

Author information

Authors and Affiliations

  1. International Atomic Energy Agency, Wagramerstr. 5, P. O. Box 100, A-1400, Vienna, Austria

    V. I. Ferronsky

  2. Water Problems Institute of the Academy of Sciences of the USSR, 13/3 Sadovaya-Chernogryazskaya, K.64, Moscow, USSR

    S. A. Denisik & S. V. Ferronsky

Authors
  1. V. I. Ferronsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Denisik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. V. Ferronsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ferronsky, V.I., Denisik, S.A. & Ferronsky, S.V. Virial oscillations of celestial bodies III. The solution of the evolutionary problem in non-newtonian time scale. Celestial Mechanics 32, 173–183 (1984). https://doi.org/10.1007/BF01231124

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01231124

Keywords

Search

Navigation