PORTUGALIAE MATHEMATICA Vol. 63, No. 1, pp. 6989 (2006) 

Non complete integrability of a satellite in circular orbitDelphine BoucherIRMAR, Université de Rennes 1,Campus de Beaulieu, F35042 Rennes Cédex  FRANCE Email: delphine.boucher@univrennes1.fr Abstract: We consider the problem of a rigid body (for example a satellite) moving in a circular orbit around a fixed gravitational center whose inertia tensor's components $A,B,C$ are positive real numbers satisfying $0<A<B\leq C=1$. We prove the non complete meromorphic integrability of the satellite using a criterion based on a theorem of J.J. Morales and J.P. Ramis. This criterion relies on some local and global properties of a linear differential system, called normal variational system and depending rationally on $A$ and $\sqrt{3(BA)}$. Our proof uses tools from computer algebra and proceeds in two steps: first the satellite {\em with axial symmetry} (i.e. $0<A<B=C=1$) then the satellite {\em without axial symmetry} (i.e. $0<A<B<C=1$). Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2006 Sociedade Portuguesa de Matemática
