  In this paper we study the linearized dynamics of spinor condensates using
the spin-node formalism developed in arXiv:0812.3403. We provide a general
method to linearize the equations of motion based on the symmetry of the
mean-field ground state using the local stereographic projection of the spin
nodes. We also provide a simple construction to extract the collective modes
from symmetry considerations alone akin to the analysis of vibrational
excitations of polyatomic molecules. Finally, we will present a mapping between
the spin-wave modes, and the wave functions of electrons in atoms, where the
spherical symmetry is degraded by a crystal field.
