ИСТИНА

We consider the dynamics of an absolutely rigid body moving on a rough horizontal plane. We assume that the plane deforms during the motion and the normal reaction in each infinitesimal area is proportional to the deformation and its rate (Kelvin-Voigt model). On the rigid body, moving along the plane, the dry friction distributed over the contact patch acts. To find the resulting friction force and torque, we integrate the infinitesimal Coulomb dry friction forces over the contact patch (like for Contensou friction). The main difference from the Contensou friction is that the contact patch, as well as the normal plane's reactions, depends on position, orientation, the velocity of the center of mass and angular velocity of the body. The particular cases are considered in details: the dynamics of a homogeneous sphere and the dynamics of the wheel modeled by a thin paraboloid. For each stage of motion of a sphere, the analytical approximations for friction force and torque are proposed. They allow solving the dynamical equations analytically and give the domains of applicability for such approximations. The precision of the approximations is discussed. Particularly, we interest if the non-holonomic constraint of motion without sliding can be realized employing distributed dry friction. The model is applied to the dynamics of a differential-drive vehicle on a horizontal plane.