### Geometrical analysis in the study of body oscillations of complex configuration in the medium flow

#### Abstract

The work is devoted to the construction and study of a mathematical model of self-oscillations of an aerodynamic pendulum in a medium flow. The model of quasi-static flow of the plate by the medium was adopted as a model of the impact of the medium on the body. According to this hypothesis, the aerodynamic forces acting on the body are applied at the center of pressure. In the problem under consideration, the center of pressure is movable relative to the plate. The equations of motion for the body in question are obtained. The transition to new dimensionless variables. The violation of uniqueness in determining the angle of attack is shown A parametric analysis of ambiguity domains is carried out. All stationary points that are solutions of the equilibrium equations are found. It is shown that in the most characteristic position of equilibrium, corresponding to the state of rest, there are no ambiguity regions. The stability of the equilibrium position corresponding to the state of rest was studied, in which the Hurwitz criterion was implemented and the stability region was depicted. It is shown that aerodynamic forces for bodies with some forms can contribute to the development of self-oscillations, and for others, attenuation. In the mathematical package MATLAB 18, a set of programs is written, which makes it possible to build areas of stability and to carry out numerical integration of the equations describing body oscillations in order to confirm the adequacy of the constructed model.

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