Celestial mechanics

, Volume 27, Issue 3, pp 215–223 | Cite as

Periodic solutions of the problem of the motion of the heavy rigid body around the fixed point in Kovalevskaya's case and their stability

  • F. M. El-Sabaa
Article
Received:
Accepted:
  • 51 Downloads

Abstract

The equations of motion of the heavy rigid body around the fixed point in Kovalevskaya's case were reduced to equations of plane motion of the fictive point under the action of some potential force. The periodic solution of the new equations was found and their stability discussed.

Keywords

Periodic Solution Rigid Body Plane Motion Potential Force Heavy Rigid Body 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Arnold, V. T.: 1963,Successes of Mathematic Sciences, No. 6.Google Scholar
  2. [2]
    Bartlett, T. H.: 1964,Publ. Copenhague Obs., No. 179.Google Scholar
  3. [3]
    Demin, V. G. and Kurchanova, M. Y.: 1977,Numerical Investigation of Periodic Orbits in Restricted Averaged Elliptic Problem of Three Bodies, Space Investigations,15, 646.Google Scholar
  4. [4]
    Hénon, M.: 1965,Ann. Astrophys. 29, No. 3.Google Scholar
  5. [5]
    Fisher, Peterson, T.: 1917,Publ. Copenhague Obs., No. 27.Google Scholar
  6. [6]
    Kolosov, G.: 1901,About One Choice of Kavalevskaya Problem of Rotation of Heavy Rigid Body Around Fixed Point, Works of Dept. Physic. Sciences Society, T. 2.Google Scholar
  7. [7]
    Poincaré, A.: Selected works.Google Scholar
  8. [8]
    Stromgren, E.: 1930,Publ. Copenhague Obs., No. 67.Google Scholar
  9. [9]
    Vagner, E. A. and Demin, V. G.: 1975, ‘About One Class of Periodic Motion of Heavy Rigid Body Around Fixed Point’,PMM 39, 929.Google Scholar
  10. [10]
    Vagner, E. A., Demin, V. G., and Isaev, J. N.: 1976,The Numerical Method of Construction of Periodic Solution of the Problem of Motion of Heavy Rigid Body with One Fixed Point, Problems of Mech. Or. Motion.Google Scholar
  11. [11]
    Ziegel, K. L.:Lectures of Celestial Mechanics.Google Scholar

Copyright information

© D. Reidel Publishing Co 1982

Authors and Affiliations

  • F. M. El-Sabaa
    • 1
  1. 1.Dept. of Mathematics, Faculty of EducationAin-Shams UniversityCairoEgypt

Personalised recommendations