| Summary: | 碩士 === 國立臺灣大學 === 天文物理研究所 === 103 === Planetary rings are fascinating systems with interesting behavior. A very comprehensive analytical study of the stability of planetary rings goes back to Maxwell when he derived for the first time a criterion for the rings of Saturn to remain linearly stable. However, we now know that Saturn does not just possess a beautiful ring system but also has several moons. Following Maxwell’s footstep, and borrowing techniques and ideas developed by other researchers, we used several approaches to investigate the motion of the particles in the ring, and combined numerical methods to check against our analytical results. Our analysis
indicates that the ring system is linearly stable if the number of particles in the ring does not exceed a certain limit. We also investigated the interaction of two particles in the ring when they get closer as a result of nonlinear interactions. We found that if the motion is more or less azimuthal (that is, the radial velocity is small), then the particles effectively repel each other. Certain quantitative results were derived concerning this behavior.
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