Consider a flywheel, mounted such that its AXIS can be rotated anywhere on the XY plane (about the Z axis), set spinning, initially oriented along the X-axis. Once spinning, the flywheel resists changes to it's axis of rotation, but if we apply enough force (red arrows), we can rotate the axis over to the Y direction and again for another $90°$, to the -X direction. After another $180°$, the direction is reversed again back to where it started. We have expended energy reversing the vector component of the wheels angular momentum twice.
My question: Where did the energy go (the energy we put into the $360°$ rotation)? What was it transformed into? That is, what evidence is there of work having been done?