Calculations of the Critical Levitron's Tilts

The magnetic surfaces' equations and their rotational transforms are derived for the axisymmetric levitron. In the nonaxisymmetric levitron the magnetic island-contour equations are obtained and some of these island contours are plotted. The critical perturbations for the complete destruction of the π-and 2π-resonances are calculated. The analytical results derived here are compared and shown to be in good agreement with the numerical results.