INTRODUCTIONThe nonconservative force field in the dynamics ofa multidimensional solid is constructed according tothe results from the dynamics of real solids under theaction of a force field in a medium. In this case, thegeneralization of equations of motion for a multidimensional solid in a similarly constructed force fieldand the receipt of, generally speaking, a full list of thetranscendental first integrals, which are expressedthrough a final combination of elementary functions,become possible. The obtained results are importantin the sense of the presence of a nonconservative forcefield in the system; previously, they were used mainlyin the potentialforce field (see, for example, [1–3]).In [4, 5], we showed the integrability of equationsof planeparallel motion of a fixed pendulum in anincidentmedium flow, when the first integral, whichis the transcendental function (in the sense of complexanalysis) of quasivelocities, was found explicitly forthe set of dynamic equations. In this case, the wholeinteraction of the medium with the solid is concentrated on that part of the surface that has the form ofthe 1D plate. Then in [5–8], the problem was generalized to the spatial case (the spherical pendulum); inthis case, the full set of transcendental first integralswas found explicitly. Here already the whole interaction of the medium with the solid is concentrated onthat part of its surface that has the shape of the plane(2D) disk. Further in [9–11], the equations of motionof 4D solids of various types of dynamic symmetry,where the force field is concentrated on that part of thesurface of the solid that has the shape of the 2D (3D)disk, were investigated; in this case, the force action isconcentrated on the 2D plane (the 1D straight line)perpendicular to this disk.FORMULATION OF PROBLEM AND THE GROUP OF DYNAMIC EQUATIONS ON LIE ALGEBRA so(