The paper has been published under the title:
Horseshoes And Nonintegrability In The Restricted Case
Of A Spinless Axisymmetric Rigid Body
In A Central Gravitational Field
in
Celestial Mechanics and Dynamical Astronomy
vol.63 no.1 1995/1996
59-79
Abstract
The purpose of this paper is to study the motion of a spinless axisymmetric
rigid body in a Newtonian field when we suppose the motion of the center of
mass of the rigid body is on a Keplerian orbit. In this case the system
can be reduced to a Hamiltonian system with configuration space a
two-dimensional sphere. We prove that the restricted
planar motion is analytical nonintegrable and we find horseshoes due to the
eccentricity of the orbit. In the case I3 / I1 > 4/3, we prove that the
system on the sphere is also analytical nonintegrable.
Keywords
Horseshoes, Analytic Integrability, Rigid Body Problem
About the Report
The report contains an extended version of the paper. It also contains
a
description of the possible Hamiltonians and of the geometry associated
to the system as well as full proof of Lemma 3.2.
February 1996
Errata
I acknowledge a gap (pointed me out by Dr.A. Burov) in the statements of
Lemma 2 and Theorem 4 (in the paper): instead of '...for any \varepsilon\in
(0,1) excepting,
at most, for a finite number of values...' it should be read '...for any
\varepsilon\in (0,\varepsilon_0) with \varepsilon_0>0 sufficiently small...'
October 1996