**4. Study of the dynamic behaviour of a magnetic top by threedimensional analysis**

We can obtain approximate guidelines for the size and shape of the levitating area by quasithree-dimensional analysis. Although the static analysis gives the 'levitating area', a magnetic top in this area may not always continue to levitate, considering the dynamic motion of the top. Furthermore, the static analysis mentioned in the previous section showed that the magnitude of the restoring force acting on the rotor magnet was small. Because the quasi-three-dimensional static analysis provides an approximate design of the magnetic top, the three-dimensional dynamic analysis should be performed to confirm whether the rotating magnetic top can maintain levitation.

In this section, how the parameters such as rotating speed, mass of the top and initial position with regard to the restoring centre affect the behaviour of the levitating magnetic top is discussed.
