We present the analytical expressions for the differential cross sections and independent partial amplitudes for elastic scattering of nuclear particles for channels with a spin value of 1/2, 1, 3/2, 2 and 5/2. The independent partial amplitudes are presented for arbitrary orbital angular momentum l and taking into account spin-orbit splitting. The analytical expressions allow one to carry out full phase shift analyses using experimental data for differential cross sections for processes with channel spins 1/2, 1, 3/2, 2 and 5/2.