TY - JOUR
T1 - Fractal planetary rings
T2 - Energy inequalities and random field model
AU - Malyarenko, Anatoliy
AU - Ostoja-Starzewski, Martin
N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/12/10
Y1 - 2017/12/10
N2 - This study is motivated by a recent 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 such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings' spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached 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 F2 of the radial cross-section F of the rings, where F is a fat fractal.
AB - This study is motivated by a recent 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 such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings' spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached 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 F2 of the radial cross-section F of the rings, where F is a fat fractal.
KW - Planetary rings
KW - dynamics
KW - fractal
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U2 - 10.1142/S0217979217502368
DO - 10.1142/S0217979217502368
M3 - Article
AN - SCOPUS:85022178407
VL - 31
JO - International Journal of Modern Physics B
JF - International Journal of Modern Physics B
SN - 0217-9792
IS - 30
M1 - 1750236
ER -