Guest lecture on variational integrators for mechatronics

A Lagrangian formulation of multidomain physical systems including multibodies, electronics, fluid power and fluid dynamics is presented.  A stable, fixed step, single stage time-stepping algorithm is then constructed using the discrete-time variational principle. The time-stepping scheme handles all forms of kinematic and dynamic constraints as well as discontinuities and inequalities such as those arising from frictional contacts, transistors, diodes, relief valves, etc.  A novel technique to handle stiff forces via ghost variables provides L-stability in the resulting semi-implicit time stepping scheme. Specific examples of systems with coupled multibody dynamics, electronics and hydraulic power will be presented.