Differential equations for librational motion of gravity-oriented rigid body

• A new notation for attitude dynamics of gravity-oriented body is introduced.
• This form generalizes equations in canonical variations.
• Both the potential and the non-potential disturbing torques are operative.
• A perturbation torque is given by a cubic approximation.
• The equations are convenient for asymptotic analysis of a body non-linear oscillations.

We consider a gravity-oriented rigid body on a circular Keplerian orbit in a central gravitational field. The motion of the body is affected by a perturbation torque given by a cubic approximation. With the inclusion of the third infinitesimal terms, we introduce a new notation for the differential equations of disturbed motion. This form generalizes the familiar equations in canonical variations extending them to the case where both the potential and the non-potential disturbing forces are operative. This form is convenient for the analysis of non-linear oscillations of a body about its center of mass with the use of the asymptotic methods of non-linear mechanics.