An approximate mathematical model is constructed for 3D motion of a body of revolution in a low-strength medium with asymmetric separation of the flow. A relationship between the kinematic and the load quantities at the interface between the body and the medium is postulated based on the isolated-element method, using exact solutions and experimental data. A criterion of ideal separation is postulated. It means that the portion of the surface facing the flow is wetted, while the shadowed region of the surface is stress-free. For the analysis of stability of the rectilinear motion of the body, the system of equations is linearized. The linearized system of equations governing the transverse motion splits into two independent systems describing the motion of the body in two orthogonal planes. In contrast to the works, which studied the stability of rectilinear motion in supposition of "frozen" axial velocity, the present paper considers the influence of braking on the stability of rectilinear motion. In the case of an unseparated flow and in the absence of tangential stresses, conditions of decrease of perturbations along the trajectory are obtained.
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