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We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings are shepherded. We consider the problem as Hamiltonian {it scattering} of a large number of non-interacting massless point particles in an effective potential. Using the existence of stable motion in scattering regions in this set up, we describe a mechanism in phase space for the occurrence of narrow rings and some consequences in their structure. We illustrate our approach with three examples. We find eccentric narrow rings displaying sharp edges, variable width and the appearance of distinct ring components (strands) which are spatially organized and entangled (braids). We discuss the relevance of our approach for narrow planetary rings.
The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific
We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non-interacting particles where open motion (escape) takes place, and includes the quasi-periodic perturbati
Euler-Poincare equations are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that the equations of mot
The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics, and can also be used to identify regions of coherence. Estimating such growth rates can be difficult, since they depend on detailed properti
We now know that the outer solar system is host to at least six diverse planetary ring systems, each of which is a scientifically compelling target with the potential to inform us about the evolution, history and even the internal structure of the bo