Chaotic and stable behaviour in the Caledonian Symmetric Four-Body Problem

Details Chaotic and stable behaviour in the Caledonian Symmetric Four-Body Problem Chaotic and stable behaviour in the Caledonian Symmetric Four-Body Problem

Jan 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004mnras.347..380s&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 347, Issue 2, pp. 380-388.

Astronomy and Astrophysics

Astronomy

20

Celestial Mechanics

Scientific paper

A special symmetric configuration of the general four-body problem called the Caledonian Symmetric Four-Body Problem is investigated. Recently, Steves & Roy have discovered a global stability parameter for the system, called the Szebehely constant. The connection between the chaotic behaviour of the phase space and the global stability given by the Szebehely constant is analysed by using the relative Lyapunov indicator (RLI) and smallest alignment indices (SALI) methods of determining regular and chaotic motion. It is found that as the Szebehely constant is increased, making the system hierarchically stable from a global point of view, the corresponding phase space becomes increasingly more regular and less chaotic.

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