VARIATIONAL-PRINCIPLES FOR CONSTRAINED SYSTEMS - THEORY AND EXPERIMENT

In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical sy stem with constraints. The resulting equations are compared. Results a re also presented from an experiment for a model system: a ball rollin g without sliding on a rotating table. Both sets of equations of motio n for the model system are compared with the experimental results. The effects of various forms of friction are considered in the nonholonom ic equations. With appropriate friction terms, the nonholonomic equati ons of motion for the model system give reasonable agreement with the experimental observations.