We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in ${\mathbb{R}}^3$. Unlike splitting methods, it is defined for all Hamiltonians and is $O\left(3\right)$-equivariant, i.e., coordinate-independent. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields a new integrable discretization of the spinning top.

• Received 17 February 2014

DOI:https://doi.org/10.1103/PhysRevE.89.061301