  This study is motivated by the observation, based on photographs from the
Cassini mission, that Saturn's rings have a fractal structure in radial
direction. Accordingly, two questions are considered: (1) What Newtonian
mechanics argument in support of that fractal structure is possible? (2) What
kinematics model of such fractal rings can be formulated? Both challenges are
based on taking Saturn's rings' spatial structure as being statistically
stationarity in time and statistically isotropic in space, but statistically
non-stationary in space. An answer to the first challenge is given through the
calculus in non-integer dimensional spaces and basic mechanics arguments
(Tarasov (2006) \textit{Celest. Mech. Dyn. Astron.} \textbf{94}). The second
issue is approached in Section~3 by taking the random field of angular velocity
vector of a rotating particle of the ring as a random section of a special
vector bundle. Using the theory of group representations, we prove that such a
field is completely determined by a sequence of continuous positive-definite
matrix-valued functions defined on the Cartesian square $F^{2}$ of the radial
cross-section $F$ of the rings, where $F$ is a fat fractal.
