A Nonlinear Model for the Rings of Saturn

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This is a nonlinear mapping for a qualitative simulation of the rings of Saturn. The model is due to Fröyland, from considerations of the Roche limit for the case of the moon Mimas.

Contributed by: Enrique Zeleny (March 2012)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Converting the differential equation of the model to a pair of finite-difference equations, we find

,

,

where is the radial distance from the center of Saturn to Mimas, and are the radial and angular positions of a ring particle after revolutions, and is a gravitation parameter derived from Newton's law of gravitation and Kepler's third law.

Reference

[1] R. H. Enns and G. C. McGuire, Nonlinear Physics with Mathematica for Scientists and Engineers, Boston: Birkhäuser, 2001.



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