We consider splitting methods for the numerical solution of differential equations with controls, arising from a marine vessel rigid body model. This model is used in simulations of offshore pipe-lay operations. The system of ordinary differential equations comprises a Coriolis centripetal term, a damping term, a term for environmental forces, a term for restoring forces and moments, and a control term. We propose a splitting into the conservative part, which is nonlinear, but completely integrable (i.e. solutions of the system can be obtained by quadrature), and the damping and control parts, which are linear and can be integrated exactly. The passivity of this system is also considered.