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Coplanarity in a torque-free axisymmetric rigid body

For principal moments

I_{1} = I_{2} = I

and symmetry-axis unit vector

e_{3}

, angular momentum and angular velocity obey

L = I ω + (I_{3} - I) ω_{3} e_{3} .

Thus

L

,

ω

, and the symmetry axis are coplanar at every instant.

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Solution