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Geometric analysis of areas of ambiguity of the angle of attack in the problem of the motion of an aerodynamic pendulum in the flow of a quasi-static medium

Abstract

Geometric analysis of areas of ambiguity of the angle of attack in the problem of the motion of an aerodynamic pendulum in the flow of a quasi-static medium

Belyakov D.V.

Incoming article date: 09.02.2023

In the article, a mathematical model of the oscillations of an aerodynamic pendulum in the flow of a moving medium is constructed and investigated. As a model of the effect of the medium on the body, the model of quasi-static flow around the plate by the medium is adopted. According to this hypothesis, the aerodynamic forces acting on the body are applied at the center of pressure. In our problem, the pressure center is movable relative to the plate. The equations of motion for the body under consideration are obtained. The transition to new dimensionless variables has been carried out. The violation of uniqueness in determining the angle of attack at points where the air velocity of the pressure center is close to zero is shown. Envelopes for some areas of ambiguity are constructed using multiple solutions of algebraic nonlinear equations derived from kinematic relations. To do this, the coordinates of the return points are determined, the solution of the equations themselves is found, and the boundaries of the areas of ambiguity are depicted. In the mathematical package MATLAB 18, a program is written that.

Keywords: body, ambiguity area, envelopes, return points