The separability of "S" depends both on the Hamiltonian and on the choice of generalized coordinates. For orthogonal coordinates and Hamiltonians that have no time dependence and are quadratic in the generalized momenta, formula_93 will be completely separable if the potential energy is additively separable in each coordinate, where the potential energy term for each coordinate is multiplied by the coordinate-dependent factor in the corresponding momentum term of the Hamiltonian (the Staeckel conditions). For illustration, several examples in orthogonal coordinates are worked in the next sections.