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Complex phenomena incorporating several physical properties are abundantwhile they are occasionally revealing the variation of power-law behaviordepending on the scale. In this present work, the global scaling-behavior ofdynamical impact of solid sphere onto elastic surface is described. Itsfundamental dimensionless function was successfully obtained by applying thedimensional analysis combined with the solution by energy conservationcomplementally. It demonstrates that its power-law behavior is given by thecompetition between two power-law relations representing inertial and elasticproperty respectively which is strengthened by scale size of sphere. Thesefactors are successfully summarized by the newly defined dimensionlessparameters which gives two intermediate asymptotics in different scale range.These power-law behaviors given by the theoretical model were compared withexperimental results, showing good agreement. This study supplies the insightsto dimensional analysis and self-similarity in general.

Intermediate asymptotics on dynamical impact of solid sphere on mili-textured surface