- #1
RickRazor
- 17
- 3
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?
"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?