An analytical conclusion of the dynamic equation for the ball moving on the rotating with the angle frequency two dimensional gutter arbitrary form is given. The both forces of the dry and viscosity friction was accounted. Due to solvation of equations system move analytically and numerical was founded of the class trajectories at neglect frictions forces.
$^1$Moscow State Aviation University (MAI)\
$^2$г. Москва, Волоколамское ш., д.4