Abstract
In this paper two cases of hierarchical arrangement common in many types of dynamical systems are considered viz. the planetary-type arrangement and the multiple stellar system type of arrangement.
The former is considered in order to investigate the applicability of the empirical stability parameters derived in the first paper of this series (Walkeret al., 1980) to planetary systems.
The second type of system has not been considered thus far in the series. A coordinate system following the method of the Jacobian coordinate system is developed for these systems. Then, following a procedure similar to that of the abovementioned paper, empirical stability parameters are derived for those systems. Finally we use the method to examine the stability of the sextuple Castor system.
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Walker, I.W. Stability criteria in many-body systems. Celestial Mechanics 29, 149–178 (1983). https://doi.org/10.1007/BF01232804
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DOI: https://doi.org/10.1007/BF01232804