27: Euler Angles
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So far, our analysis of rotational motion has been of essentially one dimensional, or more precisely one angular parameter, motion: rotating about an axis, rolling, precessing and so on. But this leaves out many interesting phenomena, for example the wobbling of a slowing down top, nutation, and so on. We need a well-defined set of parameters for the orientation of a rigid body in space to make further progress in analyzing the dynamics.
The standard set is Euler’s Angles. What you see as you watch a child’s top beginning to wobble as it slows down is the direction of the axis—this is given by the first two of Euler’s angles:
- 27.2: Angular Velocity and Energy in Terms of Euler’s Angles
- Since the position is uniquely defined by Euler’s angles, angular velocity is expressible in terms of these angles and their derivatives.
