Horseshoes and Nonintegrability in the Restricted Case of a Spinless Axisymmetric Rigid Body in a Central Gravitational Field

Details Horseshoes and Nonintegrability in the Restricted Case of a Spinless Axisymmetric Rigid Body in a Central Gravitational Field Horseshoes and Nonintegrability in the Restricted Case of a Spinless Axisymmetric Rigid Body in a Central Gravitational Field

Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995cemda..63...59b&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 63, Issue 1, pp.59-79

Astronomy and Astrophysics

Astronomy

Horseshoes, Analytic Integrability, Rigid Body Problem

Scientific paper

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 of 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 caseI 3/I 1>4/3, we prove that the system on the sphere is also analytical nonintegrable.

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