Symplectic integrators for spin systems
We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in ℝ3. Unlike splitting methods, it is defined for all Hamiltonians, and is O(3)-equivariant. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields an integrable discretization of the reduced motion of a free rigid body.