First integrals in the problem ofthe motion of a heavy rigid body about a fixed point under unilateral constraint

The problem of the existence of integrable cases of the Euler and Lagrange types, and also particular integrals of the Hess and Appel'rot type without additional assumptions on the value of the area integral, is considered for the problem of the motion of a heavy rigid body about a fixed point with constraints on the angle between the rising vertical and a vector fixed in the body.