Show that the angular velocity of a body, in terms of Euler angles f, u, and c, can be

Chapter 21, Problem 21-60

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Show that the angular velocity of a body, in terms of Euler angles \(\phi, \ \theta, \text { and } \psi\), can be expressed as \(\omega=(\dot{\phi} \sin \theta \sin \psi+\dot{\theta} \cos \psi) \mathbf{i}+(\dot{\phi} \sin \theta \cos \psi-\dot{\theta} \sin \psi) \mathbf{j}+(\dot{\phi} \cos \theta+\dot{\psi}) \mathbf{k}\), where \(\mathbf{i}, \ \mathbf{j} \text {, and } \mathbf{k}\) are directed along the x, y, z axes as shown in Fig. 21–15d.