3. a) Write down and explain the relationship between the angular velocity, w, and the angular momentum, I, for a rotating rigid body. b) Given that the rate of change of I in an inertial frame S is related to the rate of change of I in a frame R, which is rotating relative to S with angular velocity, via []s = []R + W L, show that Euler's equations for the motion of a rigid body subject to an external torque Gare G = I+ (13- 12) W3W2 G I202 + (11-13)w1W3 G3 I3W3+ (1211)ww1. and determine . = c) In what frame of reference are Euler's equations valid? Is this an inertial frame? d) A space rocket is rotationally symmetric about its length, taken to be the 3 axis in the body frame, so that I = I2 I3. The engines drive the rocket so that it rotates about its symmetry axis with constant angular velocity. However, the rocket thrust is slightly misaligned, so that there is a constant torque perpendicular to the symmetry axis. Assume that this torque is in the 2 direction in the body frame. Show that the equations of motion for the rocket in the body frame are = = Qwz G I = 0 - - [3] [6] [2] [5]