NON-INTEGRABILITY OF THE MOTION OF A POINT
MASS AROUND A PLANET OF ARBITRARY SHAPE

M.E. Sansaturio
E.T.S. de Ingenieros Industriales,
Paseo del Cauce s/n, E-47011 Valladolid, Spain
E-mail: marsan@wmatem.eis.uva.es

I. Vigo-Aguiar and J.M. Ferrandiz
Dept. de Matemática Aplicada, Escuela Politécnica Superior
E-03080 Alicante, Spain
E-mail: jm.ferrandiz@ua.es and vigo@aitana.cpd.ua.es

July 1998

Abstract:

In this paper, several results on the non-integrability of the problem of a satellite under different assumptions on the mass distribution of the primary are collected. Among them, we pay special attention to the non-integrability through meromorphic integrals of any truncation of the zonal satellite problem, as well as to that of the (J₂ + J₂₂)-problem or 'general main satellite problem'.

 

• Introduction
• Brief Summary of Yoshida's Theorem
• Non-integrability of the Truncated Zonal Satellite Problem
• The General Main Satellite Problem
• Final comments
• Acknowledgements
• Bibliography
• About this document ...

Introduction