When discussing about generalized coordinates, Goldstein says the following: "All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ quantities with the dimensions of energy or angular momentum." I understand that generalized coordinates need not be orthogonal position vectors. But what does Fourier expansion of a vector even mean? A vector has 3 coordinates, now the amplitudes of Fourier expansion are infinite. How can they be used as generalized coordinates?