Explorer-1 tipped over, but Euler equation doesn't agree

[harmyder]

$$\dot{\boldsymbol{H}} = \dot{\omega} + \boldsymbol{\omega}\times\boldsymbol H$$
Suppose body's got an impulse and 's started to rotate about its principle axis, say z, No more external moment from this time.
So, Euler equations become
$$0 = I_{xx}\dot{\omega}_x − (I_{yy} − I_{zz}) \omega_y \omega_z$$
$$0 = I_{xx}\dot{\omega}_y − (I_{yy} − I_{zz}) \omega_z \omega_x$$
$$0 = I_{xx}\dot{\omega}_z − (I_{yy} − I_{zz}) \omega_x \omega_y$$

Suppose small rotation was imparted along another axis z or y in such a way that $\omega_z >> \omega_x, \omega_z >> \omega_y.$

From differential equation we can get, we conclude that a body rotating about an axis where the moment of inertia is intermediate between the other two inertias, is unstable.

But, Explorer-1 was rotation about its longest axis - the one with smallest inertia, and tipped over due to internal forces, so rotation about axis with smallest inertia moment is unstable. Doesn't that contradict to the previous result?

 

[gtoguy97]

No, it does not contradict the previous result. It is important to note that Explorer-1 was not an isolated system, and so other forces such as gravity, air resistance, and internal forces were acting on it. These forces could have caused the instability of the rotation. Additionally, even if the body was rotating about its axis with the smallest moment of inertia, if the angular velocity in any direction was much greater than the others, then the differential equation would still predict an unstable rotation.