Advertisement

Ukrainian Mathematical Journal

, Volume 50, Issue 3, pp 377–386 | Cite as

New classes of exact solutions for a problem of many bodies that attract one another according to an arbitrary law depending on the distances between bodies

  • L. Ya. Gadomskii
  • E. A. Grebenikov
  • A. R. Gurskaya
  • N. I. Zemtsova
Article

Abstract

The existence of a 5-parameter family of exact solutions is proved for differential equations describing the motion of many bodies that attract one another according to an arbitrary law depending on the distances between the bodies.

Keywords

Elliptic Function Symmetric Solution Radius Vector Regular Polygon Initial Angular Velocity 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. A. Grebenikov, “Theorem on the existence of exact symmetric solutions in a two-dimensional Newtonian problem of many bodies,” Rom. Astronom. J., 7, No. 2 (1997).Google Scholar
  2. 2.
    V. K. Abalakin, E. P. Aksenov, E. A. Grebenikov, V. G. Demin, and Yu. A. Ryabov, A Handbook in Celestial Mechanics and Astrodynamics [in Russian], Nauka, Moscow (1976).Google Scholar
  3. 3.
    A. Wintner, The Analytical Foundations of Celestial Mechanics, Princeton University Press, Princeton (1941).zbMATHGoogle Scholar
  4. 4.
    A. D. Aleksandrov, Convex Polyhedrons [in Russian], GITTL, Moscow-Leningrad (1950).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • L. Ya. Gadomskii
    • 1
  • E. A. Grebenikov
    • 1
  • A. R. Gurskaya
    • 1
  • N. I. Zemtsova
    • 1
  1. 1.Institute of Highly Efficient Computing SystemsRussian Academy of SciencesMoscow

Personalised recommendations