Integrable systems of classical mechanics and Lie algebra. Systems with constraints

The purpose of the paper - to review the integrable haxiltonian systems of classical mechanics, on which certain restrictions (constraints) were imposed. The considered systems remain integrable ones, if the choice of these constrainsts is successful. The simplest systems of classical mechanics, on which restrictions are imposed, can refer to this case: the motion along geodesic lines on ellipsoid (or hyperboloid) surface or the motion on ellipsoid surface, given the linear central impressed force, the motion of sphere surface, given the linear impressed force