On the Issue of Studying the Stability of the Resting State under Small Oscillations of an Aerodynamic Pendulum in a Quasi-Static Medium Flow

The article considers a mathematical model of an aerodynamic pendulum mounted on two elastic elements in a quasi-static medium flow. The choice of the body-medium interaction model is crucial for modeling various applied aerodynamics problems. In this work, aerodynamic forces are formulated based on the hypothesis of stationary flow around a plate by the medium. In our problem, the center of pressure is movable relative to the plate. Using fundamental theorems of dynamics, a system of motion equations describing the mathematical model of the considered problem is obtained. Equilibrium equations are solved, and various stationary points are found. First-order approximation equations for the rest state stationary point are derived. Using the Routh–Hurwitz method, stability regions in the parameter space are constructed, and their parametric analysis is conducted. A numerical model of the pendulum’s motion is built in the MATLAB system, and the results of numerical calculations are compared with the previously obtained analytical results.