Treating a singular case for a motion of rigid body in a Newtonian field of force

Abstract

This paper presents a rotational motion of a rigid body about a fixed point in a Newtonian force field for a singular value of the natural frequency ω = 3. Such a singularity appears in [3] and has been never studied in full generality. Poincaré's small parameter method [4] is applied to investigate analytical periodic solutions, with non-zero basic amplitudes, for equations of motion of the body. A geometric interpretation of motion is given using Euler's angles to describe the orientation of the body at any instant of time.