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In this paper, we analyze the effect which the choice of a friction model hason tippe top inversion in the case where the resulting action of alldissipative forces is described not only by the force applied at the contactpoint, but also by the additional rolling resistance torque. We show that,depending on the friction model used, the system admits different firstintegrals. In particular, we give examples of friction models where the Jellettintegral, the Lagrange integral or the area integral is preserved.  We examine in detail the case where the action of all dissipative forcesreduces to the horizontal rolling resistance torque. For this case we findpermanent rotations of the system and analyze their linear stability. Also, weshow that for this friction model no inversion is observed.

The influence of the rolling resistance model on tippe top inversion