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A&A 437, 753-764 (2005)
DOI: 10.1051/0004-6361:20053031
Synchronous motion in the Kinoshita problem
Application to satellites and binary asteroids
S. Breiter1, B. Melendo2, P. Bartczak1 and I. Wytrzyszczak11 Astronomical Observatory of A. Mickiewicz University, Sloneczna 36, 60-286 Poznan, Poland
e-mail: breiter@amu.edu.pl
2 Grupo de Mecánica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain
e-mail: bmelendo@unizar.es
(Received 9 March 2005 / Accepted 18 March 2005 )
Abstract
A Lie-Poisson integrator with Wisdom-Holman type splitting is constructed for the
problem of a rigid body
and a sphere (the Kinoshita problem). The algorithm propagates
not only the position, momentum and angular momentum vector of the system,
but also the tangent vector of "infinitesimal displacements". The latter
allow to evaluate the maximum Lyapunov exponent or the MEGNO indicator
of Cincotta and Simó. Three exemplary cases are studied: the motion
of
Hyperion
, a fictitious binary asteroid with Hyperion as one of
the components,
and the binary asteroid
90 Antiope
. In all cases the attitude instability
of the rotation state with spin vector normal to an equatorial orbit influences
stability of the system at lower rotation rates. The MEGNO maps with variations
restricted to the orbital plane for position and momentum, and
to the orbit normal direction
for the angular momentum resemble usual Poincaré sections. But if no restriction
is imposed on the variations, some stable zones turn into highly chaotic regions,
often retaining the shape of their boundaries.
Key words: chaos -- methods: numerical -- celestial mechanics -- planets and satellites: individual: Hyperion -- minor planets, asteroids
© ESO 2005