A form of differential equations of the perturbed motion of a gravity-oriented rigid body

The motion of a gravity-oriented rigid body in a circular Keplerian orbit in a central gravitational field is analyzed for the case where the orientation of the body is affected by a perturbation moment allowing a quadratic approximation. A new form of differential equations of perturbed motion is obtained which generalizes the known equations in canonical variables to the case where nonpotential perturbation forces are present in addition to the potential forces. The new form of equations is convenient for analyzing the quasi-linear oscillations of a body with respect to its center of mass using asymtotic methods of nonlinear mechanics.