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=== Stable rotation around the first and third principal axis ===
Consider the situation when the object is rotating around the axis with moment of inertia <math>I_1</math>. To determine the nature of equilibrium, assume small initial angular velocities along the other two axes. As a result, according to equation (1), <math>~\dot{\omega}_1</math> is very small. Therefore, the time dependence of <math>~\omega_1</math> may be neglected.
Now, differentiating equation (2) and substituting <math>\dot{\omega}_3</math> from equation (3),
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Note that <math>\omega_2</math> is being opposed and so rotation around this axis is stable for the object.
Similar reasoning gives that rotation around the axis with moment of inertia <math>I_3</math> is also stable.
=== Unstable rotation around the second principal axis ===
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