Coupled pendulums system under control by vertical oscillations

In this paper we propose a mathematical model consisting of two inverse pendulums with an elastic coupling (by spring). We propose a dynamic programmed control of the model motion, implemented through vertical oscillations of the common pendulums pivot point. We investigate dynamics of this mechanical system, and formulated a condition for identifying stability of the system. We constructed stability zones in the spaces of the original and dimensionless parameters. Also, we obtain evolution of stability zones depending on spring stiffness values. In conclusion, we presented results of numerical software experiments for various system configurations.