Analytic Solution of Euler’s Equations of Motion for an Asymmetric Rigid Body

Abstract

The problem of the time evolution of the angular velocity of a spinning rigid body, subject to torques about three axes, is considered. An analytic solution is derived that remains valid when no symmetry assumption can be made. The solution is expressed as a first-order correction to a previous solution, which required a symmetry or near-symmetry assumption. Another advantage of the new solution (over the former) is that it remains valid for large initial conditions of the transverse angular velocities.