On periodic perturbations of uniform motion of Maxwell's planetary ring.

Details On periodic perturbations of uniform motion of Maxwell's planetary ring. On periodic perturbations of uniform motion of Maxwell's planetary ring.

Jan 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998jdde...10...47p&link_type=abstract

J. Dyn. Differ. Equ. (USA), Vol. 10, No. 1, p. 47 - 72

Physics

Planetary Rings: Perturbations

Scientific paper

The author examines the case when equally sized small moons arrange themselves on the vertices of a regular n-gon for n ≥ 7. For n ≥ 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 discussed.

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