Chaos in the reorientation process of a dual-spin spacecraft with time-dependent moments of inertia

We study the spin-up dynamics of a dual-spin spacecraft containing one axis ymmetric rotor which is parallel to one of the principal axes of the spacec raft. It will be supposed that one of the moments of inertia of the platfor m is a periodic function of time and that the center of mass of the spacecr aft is not modified. Under these assumptions, it is shown that in the absen ce of external torques and spinning rotors the system possesses chaotic beh avior in the sense that it exhibits Smale's horseshoes. We prove this state ment by means of the Melnikov method. The presence of chaotic behavior resu lts in a random spin-up operation. This randomness is visualized by means o f maps of the initial conditions with final nutation angle close to zero. T his phenomenon is well described by a suitable parameter that measures the amount of randomness of the process. Finally, we relate this parameter with the Melnikov function in the absence of the spinning rotor and with the pr esence of subharmonic resonances.