Abstract
The paper presents derivation of non-linear model of vibrations of electrically charged cloud of ice crystals. This problem is applicable as mechanical basis of a theoretical model of atmospheric optical phenomenon commonly known as the miracle of Sun. A large crystal rotation angles and a continuous distribution of charges on surface of crystals are included in deliberations. It is shown that obtained equation of non-linear model is type of equation 4 . The numerical solutions are shown for some examples of model parameter sets. They are compared with solutions of linear model available in literature. Finally, obtained theoretical results have been compared with results of observations of atmospheric phenomenon called the miracle of Sun available in literature.
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