The article deals with the conditions allowing the precession and isoconic movements of a gyrostat under the influence of potential and gyroscopic forces described by the Kirchhoff - Poisson differential equations. These movements have the following characteristic features: a constant angle between two axes, one of which is fixed in a gyrostat and the other is stationary in space; and the symmetry of mobile and immovable hodographs with respect to the plane tangent to them. A new class of precession and isoconic movements which is described by a new special integrability case of the Kirchhoff's equations is constructed.

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