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\end{cases}</math>This is shown on the animation to the left.
By inspecting Euler's equations, we see that <math>\dot\omega(t) = 0</math> implies that two components of <math>\omega(t)</math> are zero—that is, the object is exactly spinning around one of the principal axes. In all other situations, <math>\omega(t)</math> must remain in motion.
By Euler's equations, if <math>\omega(t)</math> is a solution, then so is <math>c \omega(ct)</math> for any constant <math>c > 0</math>. In particular, the motion of the body in free space (obtained by integrating <math>c\omega(ct) dt</math>) is ''exactly the same'', just completed faster by a ratio of <math>c</math>.
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