An Induced Representation Method for Studying the Stability of Saturn's Ring
arXiv:1410.5865 · doi:10.1007/s12648-016-0894-x
Abstract
MacKey constructed a set of induced representation character formulas to calculate the sum of different powers of the eigenvalues of a matrix with finite group symmetry. We show that these results of MacKey can be used to derive the stability condition, m > Cn3, of Maxwell using his symmetric model for a ring of Saturn, as a collection of n identical unit mass particles revolving round Saturn, which has mass m, in a circular orbit.