Escape from potential wells in multi-dimensional experimental systems

Abstract eng:
Predicting the escape from a potential energy well is a universal exercise, governing myriad engineering and natural systems, e.g., buckling phenomena, ship capsize, and human balance. Criteria and routes of escape have previously been determined for 1 degree of freedom (DOF) mechanical systems with time-varying forcing, with reasonable agreement with experiments. When there are 2 or more DOF, the situation becomes more complicated, and the theory of tube dynamics provides the criteria for which phase space states will escape. We report the validation of the tube dynamics theory for a 2 DOF experiment of a ball rolling on a surface. This experimental validation establishes a theoretical framework which can be exploited for purposes of control, e.g., avoiding or triggering escape or transition between metastable states in mechanical systems.

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