  A Lagrangian is introduced which includes the coupling between magnetic
moments $\mathbf{m}$ and the degrees of freedom $\boldsymbol{\sigma}$ of a
reservoir. In case the system-reservoir coupling breaks the time reversal
symmetry the magnetic moments perform a damped precession around an effective
field which is self-organized by the mutual interaction of the moments. The
resulting evolution equation has the form of the Landau-Lifshitz-Gilbert
equation. In case the bath variables are constant vector fields the moments
$\mathbf{m}$ fulfill the reversible Landau-Lifshitz equation. Applying
Noether's theorem we find conserved quantities under rotation in space and
within the configuration space of the moments.
