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The equations of motion for the rolling and gliding Tippe Top (TT) arenonintegrable and difficult to analyze. The only existing arguments about TTinversion are based on analysis of stability of asymptotic solutions and theLaSalle type theorem. They do not explain the dynamics of inversion. Toapproach this problem we review and analyze here the equations of motion forthe rolling and gliding TT in three equivalent forms, each one providingdifferent bits of information about motion of TT. They lead to the mainequation for the TT, which describes well the oscillatory character of motionof the symmetry axis $\mathbf{\hat{3}}$ during the inversion. We show also thatthe equations of motion of TT give rise to equations of motion for two othersimpler mechanical systems: the gliding heavy symmetric top and the glidingeccentric cylinder. These systems can be of aid in understanding the dynamicsof the inverting TT.

Tippe Top Equations and Equations for the Related Mechanical Systems