Vdo54 Gyroscopic Motion - Rigid Body In Space: Part 3

In this video, we continue our discussion on gyroscopic motion. We are studying the dynamics of rotating rigid bodies in space or under free fall. This is part 3 of a multi-part series where gyroscopic motion will be discussed. In this part, we explore an additional momentum conservation law that is applicable to the motion. We continue to use the vectorial interpretations of generalized momenta. To formulate this conservation equation, we discuss a critical preparatory step where the direction of the overall angular momentum conservation vector is better defined in context of the Euler angles, while not compromising the generality of analysis. The ideas of precession, relative spin, total spin and nutation are introduced and their expressions derived. We prove that these rotational speeds are constant for a freely spinning rigid body in space. In the process, we derive important identities that are valid for this gyroscopic motion.