Modeling semiregular precessions of gyrostat in the case variablegyrostatic moment

Modeling semiregular precessions of the first type assuming the variability of the gyroscopic moment is made on the basis on the Kirchhoff-Poisson’s equations, that describe the motion of a gyrostat underthe action of potential and gyroscopic forces. New classes of such motions of a gyrostat and their analyticproperties are specified.