Insight into the stability of symmetrical stellar clusters with planetary systems may be obtained by generalising the investigations of Steves and Roy on symmetrical four body problems to symmetrical N-Body problems. Analytical stability criterion valid for all time have been derived for a special symmetric configuration of the general four-body problem, called the Caledonian Symmetric Four-Body Problem (CSFBP). This problem exhibits many of the salient characteristics of the general four body problem, yet the symmetry greatly reduces the number of degrees of freedom.

The CSFBP analytical stability criterion is now generalised to n-body symmetrical problems which include problems with a mass located at the centre of mass of the system. This enables the stability of subsets such as symmetrical even number of bodies stellar clusters and symmetrical planetary systems with a large central mass/star to be investigated.