ABOUT DYNAMICS OF HEAVY BALL ON THE RUBED PLANE

It is presented the new qualitative explanation of the dynamics of the heavy ball rolling with sliding on the rubbed plane. A correlation between friction of rolling and sliding is modelling on the base experimental investigations from the tyre and railway industry. In correspondence with these results, the main influence of the rolling on the force state in the area of contact consists in the asymmetry of the diagram of the distribution of the normal contact stresses. This asymmetry is well described by the linear function with one coefficient that depends on the direction of motion and velocity of rolling and it leads to appearance of nonzero lateral component of the friction force. The main distinction of this investigating is using at the modelling of friction effects of the essentially new combined model of friction rolling, sliding and whirling. The model involves the replacement of exact integral expressions for the net vector and torque of the dry friction forces, formed with the assumption that Coulomb's friction law is valid at each point of the contact area, by appropriate Pade approximations. This approach substantially simplifies the combined dry friction modeling, making the calculation of double integrals over the contact area unnecessary.Using this model enable correctly describe the deviation of the trajectory of the ball mass center from the straightline. Practically in all previous publication of the different authors this effect had been described under additional suppositions on motion character hardly realized on the practice.