  In the paper, some concepts of modern differential geometry are used as a
basis to develop an invariant theory of mechanical systems, including systems
with gyroscopic forces. An interpretation of systems with gyroscopic forces in
the form of flows of a given geodesic curvature is proposed. For illustration,
the problem of the motion of a rigid body about a fixed point in an axially
symmetric force field is examined. The form of gyroscopic forces of the reduced
system is calculated. It is shown that this form is a product of the momentum
constant, the volume form of the 2-sphere, and an explicitly written everywhere
positive function on the sphere.
