On a pendulum motion in multi-dimensional space. Part 3. Dependence of force fields on the tensor of angular velocity

In the proposed cycle of work, we study the equations of motion of dynamically symmetric fixed $n$-dimensional rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of motion of a free $n$-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. In this work, we study that case when the force fields linearly depend on the tensor of angular velocity.