Let ¯r be the position of the center of mass of a rigid body R measured relative to a point O ?xed in aninertial reference frame N . Furthermore, Let ? be the angular velocity of a rigid body R in an inertialreference frame N . Suppose that we choose to parameterize the motion of the rigid body in terms of sixgeneralized coordinates (q1, . . . , q6). Three of the generalized coordinates (q1, q2, q3) parameterize the motionof the center of mass, that is, r = r(q1, q2, q3, t), while the other three generalized coordinates (q4, q5, q6)parameterized the orientation of the rigid body in the inertial reference frame. Starting with Koenigsdecomposition for the kinetic energy of a rigid body, determine the six Lagrange equations associated withthe generalized coordinates (q1, . . . , q6). In other words, determine the generalized forces (Q1, . . . , Q6) suchthatd/dt(?T/?q?j)??T/?qj= Qj , j = 1, . . . , 6.Assume in your solution that all rates of change are taken in the inertial reference frame and, as a result, thefollowing notation can be used: v¯ = ¯r?is the inertial velocity of the center of mass, a¯ = v¯? = ¯¨r is the inertialacceleration of the center of mass, and ? = ?? is the inertial angular acceleration of the body.Hint: In your answer to this question, you must use eulers laws”
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