On the Dynamics of a Vertical System of Masses Linked by Non-Linear Cubic Springs

摘要

In this paper we present a vertical system of rigid bodies linked one to another by non-linear springs of cubic stiffness. For this system we determine the equilibrium positions, we find a necessary and sufficient condition for the uniqueness of the equilibrium position and we prove that the equilibrium is simply stable. We also discuss the stability of the motion and the small oscillation around the equilibrium position. An application is also presented.