Figure 2 shows a Particle C attached to a two-axis gimbal. Let ax, ay, and az form a right-handed orthonormal set of basis vectors in the outer gimbal frame A with ai initially aligned with ni (i = x, y, z). Let bx, by, and bz form a right-handed orthonormal set of basis vectors in the inner gimbal frame B with bi initially aligned with ai (i = x, y, z). Let Bc be a point in the center of the inner gimbal frame B. Note that Bc is fixed in N. Let Lb be the distance from Bc to the Particle C along the unit vector by. Assume that the outer gimbal frame is rotated about ay by q1 due to a torque T1ay. There is no motor drive between the inner and outer gimbal frames. Let C have mass m and assume that the inner and outer gimbal frames may be considered massless. Assume that the local gravity vector is directed downward in the negative ny direction. Define generalized speeds as follows: u1 = q2 (1) u2 = cos(q2) q1 (2) Determine the Kinematical Differential Equations and the Dynamical Differential Equations governing the system