Synchronous motion in the Kinoshita problem

Free access article

Issue		A&A Volume 437, Number 2, July II 2005


Page(s)		753 - 764
Section		Celestial mechanics and astrometry
DOI		http://dx.doi.org/10.1051/0004-6361:20053031

A&A 437, 753-764 (2005)
DOI: 10.1051/0004-6361:20053031

Application to satellites and binary asteroids

S. Breiter¹, B. Melendo², P. Bartczak¹ and I. Wytrzyszczak¹

¹ 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

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.