Parametric analysis of stability conditions for a satellite with gyrodines. With the aid of the software LinModel elaborated on the basis of the computer algebra system Mathematica, we conduct an analysis of the dynamics for a mechanical system which represents an unguided satellite with 3 gyrodines on a circular orbit. The modeling of systems (i.e., constructing nonlinear and linearized differential equations of motion in the Lagrange second kind form), as well as the investigation of the issues of stability and gyroscopic stabilization for eight steady motions obtained, are conducted on a PC with the aid of symbolic or symbolic-numeric computations. The domains of stability and stabilization constructed are represented in either analytical form or graphic form.