[en] The probability representation of angular momentum states and the connection of the representation with the formalism of the star-product quantization procedure are reviewed. The Schroedinger equation of a general time-dependent Hamiltonian, linear in angular momentum operators, and the evolution equation for the density operator in the probability representation are solved analytically by means of the formalism of linear time-dependent constants of motion. These analytical solutions define wavefunctions and tomograms of states (generic Dicke states), which contain the atomic coherent states as a particular case. The statistical properties of these new states are also evaluated. General forms of analytically solvable Hamiltonians are established in terms of the Euler angle parametrization of the three-dimensional rotations