Stability Analysis of Small Oscillations of a Weather Vane in a Quasi-Static Medium Flow

This paper presents a mathematical model for the motion of an aerodynamic weather vane. The structure is suspended on two springs, oriented into the wind direction, and undergoes oscillations under the influence of an incident quasi-stationary flow. The equations of motion for the considered model are derived, incorporating aerodynamic forces and moments determined solely through experimental tests in a wind tunnel. The considered system admits only numerical solution. Equilibrium equations are obtained, from which various stationary points are derived. Of particular interest is the central stationary point, where the body is at rest. First-order approximation equations are derived, and stability regions are determined using the Routh-Hurwitz criterion for various parameter values. A suite of programs implemented in the MATLAB computational environment is developed for numerical simulation, confirming the obtained results.