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Andrew Mason

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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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Stephen Tashi

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You can add them as vectors. If you want to "add" them by doing 3 separate rotations, one about each axis, this is a different matter. A velocity is a rate of rotation, not a finite rotation. You'd have to define what it means to "apply each angular velocity component separately about its corresponding axis". I think you can make this definition meaningful if you think in terms of integrating angular velocity to get net displacement. As I recall, it has to do with taking the exponential of matrices.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?

Finite rotations don't commute. So if you say "perform each rotation separately about its correspondin axis" this doesn't define a unique answer. The order in which you perform them can give different results - i.e. a specific point on the rotating object can end up in different positions depending on the order of rotations. So if you treated the velocity numbers as finite rotations and performed the component rotations, you would not, in general, end up with a rotation equal to their vector sum.

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