On the problem of reducing the equations of rigid body dynamics in hyperbolic space

An affine transformation of the space of velocities of the system of equations of motion of an absolutely rigid body is given, moving relative to the center of inertia in a hyperbolic space of constant negative curvature. The movement of the body occurs under the influence of a system of gyroscopic forces and a constant servo generalized force specified by the power screw. The structure of gyroscopic forces is given by special conditions containing characteristic constant parameters (gyroscopic coefficients). For the transformed system of equations under given structural-kinetic constraints, the system is reduced to an integro-differential equation obtained with respect to one of the components of the shear rate screw. An example of exact linearization of the transformed system of equations is given.