The problem of a rigid body motion in a resisting medium with the assumption of dependence of the force moment from the angular velocity

The nonlinear mathematical model of the planar and spatial interaction of a medium to the rigid body was constructed. That model takes into account the dependency of shoulder of force from effective angular velocity of the body (the type of Struhali number). In this case the moment of force of the interaction itself is also function of the angle of attack. As it has shown for processing the experiment on the motion of the uniform circular cylinders in water, these facts necessary to take into account at modeling. At study of flat and spatial model of the interaction of the rigid body with a medium the new cases of full integrability in elementary function are found that has allowed to find the qualitative analogies between the free moving bodies in a resisting medium and the oscillations of bolted bodies in a jet flow.