# Component of angular velocity in rigid body motion -- which is right?

mcheung4
Let w = (w1, w2, w3) wrt to the body frame of a rigid body, where the body frame is right-handed orthonormal. I have gathered 2 definitions of w from different sources and I am confused at how they connect to one another. One is that the RB rotates about w through its CoM at rate abs(w), the other is that each component of w represents the rate at which the RB rotates about that particular basis axis. Does this mean we can somehow add the 3 rotations (which are about different axes) and get an equivalent rotation about some other (single) axis? Thanks!

Homework Helper
Let w = (w1, w2, w3) wrt to the body frame of a rigid body, where the body frame is right-handed orthonormal. I have gathered 2 definitions of w from different sources and I am confused at how they connect to one another. One is that the RB rotates about w through its CoM at rate abs(w), the other is that each component of w represents the rate at which the RB rotates about that particular basis axis. Does this mean we can somehow add the 3 rotations (which are about different axes) and get an equivalent rotation about some other (single) axis? Thanks!
Yes, if there is a simple finite rotation. That is Euler's rotation theorem. See:http://vmm.math.uci.edu/PalaisPapers/EulerFPT.pdf

Where there is continual rotation about more than one axis, one axis of rotation will rotate about another axis, which means the axis will precess. Warning: that analysis of rotational motion can be rather complicated and difficult.

AM

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