Attitude Motion of Asymmetric Dual-Spin Spacecraft

An exact analytical solution is obtained for the attitude motion of a class of asymmetric dual-spin spacecraft which may be modeled as free systems of two rigid bodies, one asymmetric and one axisymmetric. The type system considered constitutes a gyrostat. The symmetry axis of the axisymmetric rigid body and either the axis of the largest, or that of the smallest, moment of inertia of the system are assumed to be parallel. Zero internal torque is assumed also. The integral of rotational angular momentum of the system, an integral of energy of the system and the constancy of the symmetry-axis component of rotational angular momentum of the symmetric body are used to reduce the solution of the problem to quadratures, which are evaluated in terms of Jacobian elliptic functions and elliptic integrals. Internal resonances, which may exist in imperfect spacecraft, are discussed. Resonance curves, constructed using the exact solution, are presented for a typical, asymmetric, dualspin spacecraft.