Chaotic and stable behaviour in the Caledonian Symmetric Four-Body Problem
Originally published in: Monthly Notices of the Royal Astronomical Society (2004), 347 (2), pp.380-388.
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.
A. Széll, B. Érdi, Z. Sándor, and Bonnie Steves. "Chaotic and stable behaviour in the Caledonian Symmetric Four-Body Problem" Monthly Notices of the Royal Astronomical Society (2004).
Available at: http://works.bepress.com/bonnie_steves/4