New classes of particular solutions to one problem on gyrostat motion

The paper studies the existence of two new classes polynomial solutions to differential equations related problem gyrostat motion with a fixed point in magnetic field, taking into account Barnett-London effect. A common feature structure these is that functions set invariance relations for unit vector components symmetry axis active force fields are either rational first component specified or auxiliary variable. Three particular under consideration constructed. These described by obtained inversion hyperelliptic integrals. It has been proved another constructed solution structures study, which movement property precession, case known solution.