Experimental comparison between nonholonomic and vakonomic mechanics in nonlinear constrained systems

It is known that there exist two types of methods to derive the equations of motion for mechanical systems subject to constraints. They are called nonholonomic and vakonomic mechanics. Lewis and Murray showed some simulations for two models of a ball on a rotating table, which are modeled by nonholonomic and vakonomic mechanics, and carried out experiments using a laboratory equipment. They concluded that nonholonomic mechanics provides a good model for a ball on a rotating table. However, they did not show the details of experiments, and hence there exist some ambiguous parts in their paper. Hence, we perform additional experiments for a ball on a rotating table using a laboratory equipment of a ball on a rotating table, and compare simulation and experimental results. In this manner, we can confirm that nonholonomic mechanics shows better performances in comparison with vakonomic mechanics as Lewis and Murray asserted.