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We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates inthe homogeneous-local-spin-orientation approximation, that is withunidirectional local magnetization. By analytically calculating the exacteffective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbertequation for the dissipative condensate magnetization dynamics, and show how itleads to the Stoner-Wohlfarth model of a uni-axial ferro-magnetic particle,where the latter model determines the stable magnetization patterns andhysteresis curves for switching between them. For an external magnetic fieldpointing along the axial, long direction, we analytically solve theLandau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that themagnetic dipole-dipole interaction {\it accelerates} the dissipative dynamicsof the magnetic moment distribution and the associated dephasing of themagnetic moment direction. Under suitable conditions, dephasing of themagnetization direction due to dipole-dipole interactions occurs within timescales up to two orders of magnitude smaller than the lifetime of currentlyexperimentally realized dipolar spinor condensates, e.g., produced with thelarge magnetic-dipole-moment atoms ${}^{166} \textrm{Er}$. This enablesexperimental access to the dissipation parameter $\Gamma$ in theGross-Pitaevski\v\i~mean-field equation, for a system currently lacking acomplete quantum kinetic treatment of dissipative processes and, in particular,an experimental check of the commonly used assumption that $\Gamma$ is a singlescalar independent of spin indices.

Stoner-Wohlfarth switching of the condensate magnetization in a dipolar spinor gas and the metrology of excitation damping