To stay with finite (as opposed to infinite) degrees of freedom, Goldstein might have a [complex discrete Fourier transform (DFT)](https://en.wikipedia.org/wiki/Discrete_Fourier_transform)
$$ {\bf r}_j(t)~=~\sum_{k=1}^N e^{2\pi i jk/N }{\bf q}_j(t)$$
(or a real version thereof) in mind. Here the amplitudes ${\bf q}_j(t)$ play the role of generalized coordinates. This is for instance useful for finding normal modes of lattice models.