Celestial Mechanics and Dynamical Astronomy

, Volume 55, Issue 4, pp 323–330 | Cite as

About the periodic solutions of a rigid body in a central Newtonian field

  • F. M. El-Sabaa
Article

Abstract

The equations of motion of a rigid body about a fixed point in a central Newtonian field is reduced to the equation of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid.

The construction of periodic solutions near the equilibrium points, by using the Lipaunov theorem of holomorphic integral, is obtained and the necessary and sufficient conditions for the stability of the system are given.

Key words

Periodic orbits rigid body dynamics stability 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • F. M. El-Sabaa
    • 1
  1. 1.Department of Mathematics, Faculty of EducationAin Shams UniversityEgypt

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