Development of Stability Domains for Various Stationary Points in the Problem of an Aerodynamic Pendulum in a Medium Flow

This paper presents the construction and investigation of a mathematical model of an aerodynamic pendulum in a medium flow. To model the aerodynamic forces, the hypothesis of quasi-static flow around a plate by the medium is employed. The equations of motion are obtained in dimensionless variables, describing the regimes of small oscillations of the aerodynamic pendulum. A violation of uniqueness in determining the angle of attack is demonstrated. A graphical and numerical investigation of the solutions to the equilibrium equations is carried out, and various nontrivial stationary points are found. For the identified stationary points, stability regions are constructed using the Routh–Hurwitz method. A software package has been developed in the MATLAB mathematical environment, enabling the construction of stability regions and the numerical integration of the equations describing the body’s oscillations.