have a question about the dynamics of a suspended horizontally rotating wheel subjected to gravitational force like in following picture I took from here:
At the beginning the wheel has an angular momentum $\vec{L}:=L \vec{e_x} $ in the horizontal plane, which coincides with the axis of rotation (considered as the initial condition before the gravitatitional force start to act). Then we let the gravitation act on the wheel and we observe that the wheel axis performs a precession movement on the horizontal plane.
For sake of completeness there is also a video discussing it.
The theory says that gravity exerts torque $M \vec{e_y}$ (directing into the drawn 2d plane) on the wheel around the mounting point as a fixed point, so that according to the angular momentum law, in an infinitely small period of time $\tau$ the new angular momentum $ L' $ has the value $\vec{L} + \Delta L = \vec{e_x } + \tau \cdot M \vec{e_y} $ also rotates infinitesimally in the horizontal xy plane. That's clear so far.
Question: What I don't understand is why does the axis of rotation follow presisely this movement, ie tries to align with respect the direction of the angular momentum evolving directed by gravitational force on the horizontal plane to $\vec{L} \to \vec{L} + \Delta\vec{L}$ as showed in the picture? In general,the angular momentum and the axis of rotation of the considered rigid body are not necessarily parallel. Only if the rotation is about one of it's major axes.
So the question is not why the angular momentum moves that way (it's clear to me), but why the angular velocity pseudovecor of the wheel "strives" towards this alignment with respect to the direction of the angular momentum? Which principle forces this behaviour?