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This paper considers a mathematical model of oscillations of an aerodynamic pendulum in the flow of a moving medium. A model of quasi-static flow around a plate by the medium is adopted as the model of the medium’s influence on the body. According to this hypothesis, aerodynamic forces acting on the body are applied at the center of pressure. The equations of motion are derived and expressed in new dimensionless variables. The violation of the uniqueness of the angle of attack at certain points is demonstrated. Envelopes are constructed for some regions of ambiguity. To achieve this, multiple solutions of algebraic nonlinear equations derived from kinematic relationships are obtained. Initially, the coordinates of return points are determined, then the solutions of the equations themselves are found, and the boundaries of the ambiguity regions are depicted. A MATLAB 22 program is developed to construct the upper and lower boundaries of the ambiguity regions.

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Investigation of Ambiguity Regions in Angle of Attack in the Problem of Oscillations of an Aerodynamic Pendulum in a Medium Flow

  • 会议论文

  • 发表日期：

    2025年

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  • D. V. Belyakov

摘要

This paper considers a mathematical model of oscillations of an aerodynamic pendulum in the flow of a moving medium. A model of quasi-static flow around a plate by the medium is adopted as the model of the medium’s influence on the body. According to this hypothesis, aerodynamic forces acting on the body are applied at the center of pressure. The equations of motion are derived and expressed in new dimensionless variables. The violation of the uniqueness of the angle of attack at certain points is demonstrated. Envelopes are constructed for some regions of ambiguity. To achieve this, multiple solutions of algebraic nonlinear equations derived from kinematic relationships are obtained. Initially, the coordinates of return points are determined, then the solutions of the equations themselves are found, and the boundaries of the ambiguity regions are depicted. A MATLAB 22 program is developed to construct the upper and lower boundaries of the ambiguity regions.