The integral variational principles for embedded variation identity of high-order nonholonomic constrained systems

Abstract

In this article, from the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems, three kinds of dynamics for high-order nonholonomic constrained systems are obtained, including the vakonomic dynamical model, Lagrange-d'Alembert model and a new one if utilizing respectively three kinds of conditional variation to them. And the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems is also fitted for the general nonholonomic systems when the constrained equation is reduced to a first-order one. Then, the vakonomic dynamic, Chetaev dynamics and a new model of general nonholonomic systems can also be obtained. Finally, two illustrated examples are used to verify the validity of the theory.