Mechanics of scourge: Shock wave generation. An application to macroeconomics

The herder’s scourge/whip motion dynamics is modeled and analyzed. Using generalized functions the potential and energy of the shock wave packet produced by the scourge motion are determined in terms of parameters of scourge and its initial velocity. The scourge is shown to be similar to a specific variable-mass rocket. This model is suggested as well for thundercracks. The reverse motion of scourge is applied to macroeconomics for modeling the growth of wealth characterized by the market index variation in time including bull, bear, and bull-bear markets.