CLARIFICATION TO STABILITY OF THE DEFORMED SYSTEMS

At the design stage of machine parts and engineering structures necessarily validated terms of strength, stiffness and stability. The execution conditions for the stability guarantees a state of equilibrium of machine elements and systems. The problem of stability of circular bodies, which rely on other convex body is quite topical in the areas of mechanics of the deformed body. In existing scientific works devoted to this problem, is not taken into account deformation of the bodies in contact, and consequently, not taken into account the rolling resistance between the bodies. Taking into account the influence of the rolling resistance in the study of equilibrium of bodies enables more accurate determination of the limiting position of equilibrium. Purpose.To improve and generalize the method of calculation of stability ball (cylinder) on convex surfaces, using the results of the analysis of the influence of physico-mechanical characteristics of the material and geometry of the bodies which are in contact, to limit their equilibrium position. Conclusion. Studies have shown that taking into account the real geometrical parameters and physical-mechanical characteristics of materials when considering the equilibrium state of a ball or cylinder on convex surfaces increases the angle of equilibrium, and the maximum value of the angle at the same radii and diagrams touch the ball?ball, ball?cylinder, cylinder?cylinder is the same. The dependences of the maximum deflection angle of the ball with its stability on the radius of the center of mass of the ball or cylinder.