How to sample linear mechanical systems

Abstract

Variational integrators is a a new discretization technique of the equations of motion of a mechanical system introduced by Veselov and further developed by J. Marsden an co-workers, which is now widely used by numerical analysts working in various applied fields. This discretization technique, unlike the usual discretization procedures familiar in control, e.g. zero-order-hold, can lead to simple and well-conditioned transformation formulas for the recovery of the continuous time parameters from the discretized model.We discuss variational integrators for linear second order mechanical systems and show that physically meaningful properties of the continuous-time model, like passivity, are preserved. Variational integrator discretization is also shown to provide well-conditioned models for the identification of continuous-time second-orders systems starting from measured data. © 2010 Springer-Verlag Berlin Heidelberg.