On Ziegler Effect with Arbitrary Large Viscous Friction

Abstract

We study a mechanical system with two degrees of freedom simulating the motion of rotor blades on an elastic bushing of a medium-sized helicopter. For small values of some problem parameters, the destabilizing effect due to small linear viscous friction forces has been studied earlier. Here we study the problem with arbitrary large friction forces for arbitrary values of the problem parameters. In the plane of parameters, the regions of asymptotic stability and instability are calculated. As a result, necessary and sufficient conditions for the existence of a destabilizing effect under the action of potential, follower forces and arbitrary friction forces have been obtained. It is shown that, if some critical friction coefficient $k_{*}$ tends to infinity, then there exists a Ziegler area with arbitrarily large dissipative forces.