Stability of Dual Pendulum with Viscous-Elastic Elements under Loading by Tracking and Conservative Forces

The Ziegler pendulum with viscous-elastic joints that is additionally loaded with a conservative force is considered. A problem of stability of the equilibrium position is solved in the linear statement. Destabilization of the system equilibrium by small dissipative forces is shown. A value of the conservative force is found at which the destabilization does not occur. The behavior of real parts of the characteristic equation roots is investigated depending on values of forces acting upon the system. A critical case of a single zero root is considered.