  Equations of motion of an axially symmetric sphere rolling and sliding on a
plane are usually taken as model of the tippe top. We study these equations in
the nonsliding regime both in the vector notation and in the Euler angle
variables when they admit three integrals of motion that are linear and
quadratic in momenta. In the Euler angle variables $(\theta,\phi,\psi)$ these
integrals give separation equations that have the same structure as the
equations of the Lagrange top. It makes it possible to describe the whole space
of solutions by representing them in the space of parameters $(D,\lambda,E)$
being constant values of the integrals of motion.
