A symplectic integrator for molecular dynamics on a hypersphere

We present a reversible and symplectic algorithm called ROLL, for integrating the equations of motion in molecular dynamics simulations of simple fluids on a hypersphere \(\mathcal{S}^d\) of arbitrary dimension \(d\). It is derived in the framework of geometric algebra and shown to be mathematically equivalent to algorithm RATTLE. An application to molecular dynamics simulation of the one component plasma is briefly discussed.