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This question was posed by John Zwart in the American Journal of
Physics, Vol. 70, No. 2, p. 105, February 2002 but has not been
answered since:

" According to the classical kinetic theory of gases, a rigid
nonlinear poly-atomic molecule has six degrees of freedom; three
translational and three rotational. The equipartition theorem states
that "each degree of freedom has associated with it-on average-an
energy of (1/2)kT per molecule."

For a free rotation of a rigid body with three nonequal moments of
inertia about its principal axes, solving the Euler equations shows
that while rotations about the axes with the largest and smallest
principal moments are stable, a rotation about the intermediate moment
axis is not. Any perturbation in a rotation about this intermediate
moment axis grows quickly, leading to a rotation about one of the
other axes. If we apply this result to a rigid poly-atomic molecule,
it appears that one degree of freedom could not, on average, have as
much energy as the other two rotational degrees. Why not?"

Can somebody here offer an answer?

Thanks.