Can Uniformly Dense Sphere in Vacuum Rotate on Two Axes Simultaneously?

Summary A rigid body’s orientation in space is always described by a single angular velocity vector about one axis. In fact, Euler’s rotation theorem tells us any rotation at an instant can be represented by one axis and an angle. Thus a sphere “spinning” cannot have two independent spin axes at the same time – any attempt to decompose it yields a single effective rotation axis. A uniform solid sphere has an isotropic inertia tensor (principal moments $I_1=I_2=I_3$), so its angular momentum $\ma