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The effect of forces acting upon a ferromagnetic rotational ellipsoid located in a homogeneous rotating magnetic field is considered. Lagrange’s equations of the second kind connecting the motion parameters of a particle with torques acting upon it are composed. A non-homogeneous nonlinear autonomous system of second-order differential equations is obtained. That system is not solvable by quadrature. A solution by fixed-point method is proposed in this paper.

Mathematics Subject Classification (2010): 74H20, 74H25, 47H10, 58C30.

Keywords: Fixed point, Lagrange’s equations, differential equations.