An Induced Representation Method for Studying the Stability of Saturn's Ring
Soumangsu Bhusan Chakraborty, Siddhartha Sen
TL;DR
This paper applies induced representation character formulas to derive a stability condition for Saturn's ring model, linking group symmetry methods with planetary ring stability analysis.
Contribution
It introduces a novel application of MacKey's induced representation formulas to determine the stability criterion of Saturn's ring model.
Findings
Derived stability condition m > Cn^3 for Saturn's ring
Connected group representation theory with planetary ring stability
Provided a mathematical framework for analyzing ring stability
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.
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