Rotational Stability -- from Eric Weisstein's World of Physics

Rotational Stability

Consider a rotating body, and determine it principal moments of inertia with . The rotation about C (largest principal axis) is stable, rotation about B (middle principal axis) is unstable, and rotation about A (smallest principal axis) is "mostly" stable. A parameter describing the degree of stability is given by

for rotation about the C-axis or

for rotation about the A-axis.

Precessional Constant, Principal Moments of Inertia

References

Chandrasekhar, S. Ellipsoidal Figures of Equilibrium. New Haven, CT: Yale University Press, 1969.

Greenspan, H. P. The Theory of Rotating Fluids. London: New York: Cambridge University Press, 1968.

Kopal, Z. Figures of Equilibrium of Celestial Bodies, with Emphasis on Problems of Motion of Artificial Satellites. Madison: University of Wisconsin Press, 1960.

Lyttleton, R. A. Theory of Rotating Fluid Masses. Cambridge, England: Cambridge University Press, 1953.

Rabier, P. J. and Oden, J. T. Bifurcations in Rotating Bodies.

Weisstein, E. W. "Books about Rotational Figures of Equilibrium." http://www.ericweisstein.com/encyclopedias/books/RotationalFiguresofEquilibrium.html.