This is an example to help me understand the Newton / Euler laws.

Imagine a rigid object rotating in free space, since there are no external forces acting on it then by the first law:

- Linear momentum in x dimension = constant.
- Linear momentum in y dimension = constant.
- Linear momentum in z dimension = constant.
- Angular momentum about x axis = constant.
- Angular momentum about y axis = constant.
- Angular momentum about z axis = constant.

Imagine the object is shaped as follows, for simplicity assume most of its mass is concentrated at its ends:

Assume it is rotating about the y axis (wx = wz = 0). Then centifical forces would be generated which would tend to rotate it until the masses are aligned at 90 degrees to the y axis. If this happened then the rotation would slow down to keep wy * Iyy constant.

But what I don't understand is: while it is making this transition it must have some instantaneous rotation in the wx and wz directions? which appears to contradict the conservation laws? or does it ? in the position shown it would have an apparent clockwise rotation in the z axis, but then when it has rotated 180 degrees in the y axis it appears to be rotating anti-clockwise in the z axis. So perhaps this transition does not involve rotation about x and z?

Or is this a gyroscope issue? and will precession type forces be generated to cancel out the cenrifical forces and will it continue to rotate off axis?

So how can I write equations for the motion of an object without any external forces?

I originally thought that I could define the motion with the constants vx,vy,vz, wx,wy and wz. Where v is the velocity of the centre of mass and w is the rotation about the centre of mass. However this does not seem to be sufficient to describe this movement?

The conservation laws don't appear to be enough to describe what is happening here? its as if some other quantity is being minimised or maximised?

Can anyone help clarify my thinking?

This example is to help me understand the concepts of dynamics here