Many recent observations have shown that resonances have a wide variety of effects in planetary rings: spiral waves, gaps, confinement, sharp edges, arcs. While resonances are known to be associated with such structures, the role of inter-particle collisions is still poorly understood, although necessary to explain the long term evolution of the rings.
In an effort to better understand the associated dynamics, we have performed numerical simulations of colliding particles orbiting a massive central planet. The code simulates the 3-D motion of 100 identical spherical particles orbiting a massive cental body and suffering inelastic collisions while being perturbed by one or more satellites.
We used this code to explore in more details the dynamics of are rings, and to explain in particular the reeent observations of are structures around Neptune. Clusters of particles at a satellite’s Lagrangian point {L4 or L5) are shown to be dispersed by dissipative effects. However, a second satellite can stabilize the system by providing sufficient energy through a Lindblaďs
resonance m±l:m. Other dynamically equivalent configurations (e.g. only one satellite, but with an eccentric orbit) can also stabilize are sytems, in accord with current analytical models.
We examine the roles of collisions at Lindblad and corotation resonances in various cases. Arcs remain at the potential maxima created by the corotations. However, stability requires that the satellites’ masses be within a limited range: small satellites cannot provide enough energy while large ones give too much, so the arc can disperse.
The method to determine the inclination distribution of zodiacal particle orbits according to 3D-density models of zodiacal dust presented by Giese and Kneißel (1987, this volume) is briefly discussed. The results show that models with additional bulges at the solar poles bear an isotropic component of the inclination
distribution amounting up to 20% of all orbits, whereas infrared models show almost no isotropic component. The existence of an isotropic component for zodiacal dust orbits is questioned by comparison with the orbital elements of meteoroidal particles which serve as a source for the zodiacal dust by mutual collisions