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== Geometric analysis ==
[[File:Intersecting ellipsoids.gif|thumb|upright=1.5|A visualization of the instability of the intermediate axis. The magnitude of the angular momentum and the kinetic energy of a spinning object are both conserved. As a result, the angular velocity vector remains on the intersection of two ellipsoids. Here, the yellow ellipsoid is the angular momentum ellipsoid, and the expanding blue ellipsoid is the energy ellipsoid.]]During motion, both the energy and angular momentum-squared are conserved, thus we have two conserved quantities:<math display="block">\begin{cases}
2E = \sum_i I_i \omega_i^2\\
L^2 = \sum_i I_i^2 \omega_i^2
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