On the Stability of Equilibrium of a Mechanical System with Tracking, Potential, and Small Dissipative Forces

Abstract

We consider a holonomic non-conservative mechanical system with two degrees of freedom that simulates the motion of a vane on the elastic bushing of the helicopter’s main or rudder screw in the thrust plane. The system experiences the action of potential, non-conservative positional forces and linear dissipative forces, which describe the effect of internal friction during deformation of the vane and the effect of the external environment. A multiparameter family of stationary solutions of the model is described, and an investigation of Lyapunov’s stability of a trivial solution in the presence of small linear friction forces is carried out. Ziegler’s areas were plotted for different values of the problem parameters.