Dynamic and static properties of the LJ fluid at a density and temperature close to the triple point are determined and compared for molecular dynamics computer simulations using (N, V, E), (N, V, T), (N, P, H) and (N, P, T) ensembles. As expected, the mean values of thermodynamic properties for all the different ensembles show good agreement. For the velocity autocorrelation function and the time dependence of the mean square displacement it is shown that the constant temperature and/or constant pressure algorithms used produce results which are identical, within statistical accuracy, to those obtained using the constant energy ensemble. The equations of motion are presented in a readily implementable form.