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On Periodic Perturbations of Uniform Motion of Maxwell's Planetary Ring
Authors:Felino G. Pascual
Affiliation:(1) Department of Mathematics/Statistics, Winona State University, Winona, Minesota, 55987
Abstract:We examine the case when equally sized small moons arrange themselves on the vertices of a regular n-gon for nge 7. For n ge 4, there are at least 3 pure imaginary characteristic exponents, each of which has multiplicity = 1, a surprising result that makes it possible to apply the Lyapunov center theorem to verify the existence of some periodic perturbations. For sufficiently large n, when the regular n-gon is the unique central configuration, the number of families of periodic perturbations is at least equal to 2nlfloor(n + 1)/4rfloor, where lfloorxrfloor is the greatest integer less than or equal to x.
Keywords:Lyapunov center theorem  Maxwell's planetary ring  periodic perturbations  relative equilibrium
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