eng Science and Education Publishing Applied Mathematics and Physics 2014-02-07 2 1 19 26 10.12691/amp-2-1-6 AMP2014216 article Artur Wirowski artur.wirowski@p.lodz.pl 1 Department of Structural Mechanic, Technical University of Lodz, Lodz, Poland The paper includes the derivation of the equation of the two-dimensional, dynamic behavior of electrically charged cloud of ice crystals. A large crystal rotation angles and a continuous distribution of charges on the surface of the crystals are included in deliberations. Finally, possible solutions of model equation are discussed and compared with solutions available in the literature. The resulting model can be used as a mechanical basis for optic models of the atmospheric phenomenon called the “miracle of the sun”. http://pubs.sciepub.com/amp/2/1/6/amp-2-1-6.pdf the miracle of the Sunfinite difference methodnon-linear vibrationsmathematical modeling