Abstract
Problems of motion of a rigid body with a fixed point are one of the urgent problems in classical mechanics. A feature of this problem is that, despite the important results achieved by outstanding mathematicians in the last two centuries, there is still no complete solution. This paper obtains an analytical solution of the problem of motion of an axisymmetric rigid body with variable inertia moments in resistant environment described by the system of nonlinear differential equations of L. Euler, involving the partial discretization method for nonlinear differential equations, which was built by A. N. Tyurekhodjaev based on the theory of generalized functions. To such problems belong gyroscopic instruments, in particular, and especially gyroscopes.