A mechanical realisation of a symplectic numerical method with large step-size

We show that a mechanical model of a pin-jointed linked structure is exactly equivalent to a symplectic Euler discretisation of a Hamiltonian ODE system. The step-size of this discretisation relates to a mechanical quantity which can take arbitrary values. Thus we may explore the behaviour of the symplectic Euler method in regions not normally considered appropriate for a numerical scheme and investigate the use of backward error analysis in describing the behaviour of the pin-jointed structure.