In three dimensions, the rotation around one axis can affect the distribution of mass around other axes of rotation. That change in the moment of intertia causes acceleration, which can result in chaotic motion even without the addition of any outside forces.
Reminds me of the tumbling T-handle. A small tool is spun up in one axis, and due to some interesting physics, ends up flipping over on another axis every few seconds.
It's about angular momentum and happens whenever the axis of rotation differs - even slightly - from the semi-major axis. Interaction with a fluid is not necessary.
You can demonstrate it at home with your smartphone (or, more canonically, a tennis racket), and see for yourself that the tumbling happens much too quickly to be explained by whatever force the air is imparting.
What do you mean by "other axes of rotation"? As long as the object is rigid and not acted upon by external forces, its axis should never change, since both the direction and magnitude of angular momentum are conserved.
Wikipedia talks of "chaotic rotation" of astronomical objects, but only over long timescales due to gravitational interactions and thermal effects. On short timescales, its axis shouldn't change much at all, unless you bump into it and apply an off-axis torque.
Alright, that makes more sense, the trick is that the (conserved) angular momentum vector need not be parallel with the angular velocity vector, the simplest example being torque-free precession [0]. It doesn't help that most examples of non-constant angular velocity have external forces in the mix to confuse the reader.
