Abstract
In this paper, we discuss an asymmetric gyrostat with a rotor to which a mass point is attached, this breaks the symmetry and perturbs the integrable system periodically. We take this system as a Euler–Poinsot motion perturbed by a small periodic excitation, and apply the Melnikov method to determine the intersection of the stable and unstable manifold of the system's hyperbolic point, since, this is the cause of chaos. We also manifest the chaotic motion in angular momentum space by the Poincaré surface of section. The stability about the rotating axis is also showed in the portrait of the Poincaré surfaces of section.
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