where ψ, φ, θ are the Euler angles, θ is the angle between the vertical z -axis and the top's z ′ -axis, ψ is the rotation of the top about its own z ′ -axis, and φ the azimuthal of the top's z ′ -axis around the vertical z -axis. The principal moments of inertia are I 1 about the top's own x ′ axis, I 2 about the top's own y ′ axes, and I 3 about the top's own z ′ -axis. Since the top is symmetric about its z ′ -axis, I 1 = I 2. Here the simple relation for local gravitational potential energy V = Mgl cos θ is used where g is the acceleration due to gravity, and the centre of mass of the top is a distance l from its tip along its z ′ -axis.