Simulation of motion stability of deformed elongated bodies based on variations of angular velocities in roll

The class of moving objects, which are bodies of revolution, which for some reason have undergone irreversible deformations of the hull, is considered.
The immediacy of the problem being studied has to do both with the need to study the dynamics of such objects and the insufficiency of the studies already conducted, which are mainly focused on the study of the effects of aeroelasticity or mass asymmetry and do not affect the dynamics of bodies with irreversible deformations.
The problem of the motion stability of the considered objects, including the process of interaction of the longitudinal and lateral movements of the deformed body, is formulated. Particular attention is paid to the movement of the curved body with rotation about the roll and the identification of the presence of critical roll velocities. It is noted that for the case of passive movement there are three possible reasons for this interaction: aerodynamic, kinematic, inertial.
A theoretical approach has been developed that takes into account the specific features of the geometry of deformed bodies. The approach made it possible in practical studies to determine the allowable deformation levels and its relationship with the motion parameters of deformed bodies.
The stability analysis was carried out based on the stability criteria of the system solutions describing the body movement according to the Routh–Hurwitz criterion. The body parameters, which have a varying degree of influence on the stability of movement, are determined. In a more general case, the curve of the stability boundary for a given angular velocity in roll will have a more complex form than a simple hyperbola.
The possibility of obtaining a direct solution to a nonlinear to the determining parameters equation is also shown. It will make it possible to obtain the dependences of the critical heel velocities and stability ranges on these parameters.
Mathematical modeling based on the developed techniques, carried out for direct and curved bodies, showed that the body curvature has a significant effect on the displacement of the lines of derivative pitch moments in the angle of attack and the moment of sliding in the angle of slip relative to the limits of stability. The range of angular velocities for the roll is determined, in which a loss of stability is observed for the curved body. The effect of variations in the angular velocity and the relative change in the derivative of the yaw moment coefficient in the slip angle on the value of the determining factor from the stability conditions for the direct and curved bodies is analyzed. It is shown how the curvature of the body leads to a shift of the saddle point. The effect of a change in the Mach number on the determining coefficient of characteristic equations is analyzed.