2. An axisymmetric satellite, with symmetry axis , is not subject to external torques and no energy dissipation occurs. At a given time to, the satellite rotates with angular velocity components given by 0 = 0.02 sec 20 = -0.05 sec @30 = 0.5 sec whereas the principal inertia moments are I =I=I=200 kg-m I = 250 kg.m The inertial axis is aligned with the angular momentum Hc, and the Euler angles (sequence 3-1-3) are employed to describe the instantaneous spacecraft orientation. The precession angle y at to equals 60 deg. (a) Calculate the angular momentum components along the principal axes of inertia at to - (b) Evaluate the nutation angle and the spin angle at t - (c) At to, obtain the rotation matrix R, where B () is the reference frame B+I associated with the principal axes of inertia and I () is the inertial frame. At to +60 sec, an impulsive torque (with duration of 1 sec) is applied, such that the subsequent attitude motion is pure spin about body axis e3. (d) Determine direction (in the body axes frame ()) and magnitude of this impulsive torque.