  The equations of motion for the rolling and gliding Tippe Top (TT) are
nonintegrable and difficult to analyze. The only existing arguments about TT
inversion are based on analysis of stability of asymptotic solutions and the
LaSalle type theorem. They do not explain the dynamics of inversion. To
approach this problem we review and analyze here the equations of motion for
the rolling and gliding TT in three equivalent forms, each one providing
different bits of information about motion of TT. They lead to the main
equation for the TT, which describes well the oscillatory character of motion
of the symmetry axis $\mathbf{\hat{3}}$ during the inversion. We show also that
the equations of motion of TT give rise to equations of motion for two other
simpler mechanical systems: the gliding heavy symmetric top and the gliding
eccentric cylinder. These systems can be of aid in understanding the dynamics
of the inverting TT.
