Nonholonomic Dynamics, Several Basic Questions

This paper consists of five chapters. The first chapter presents a comprehensive study of nonholonomic dynamics. They are studied that the nonlinear problem and un-determinate problem of virtual displacement in nonholonomic system in the second chapter. In chapter 3, they are studied that Chetaev model and Vacco model in nonholonomic system. A unified form of Hamilton principle in intrinsical linear nonholonomic system is studied in chapter 4. Lastly, this paper presents the conclusion and the prospects of the nonholonomic dynamics.The definitions of intrinsical linear nonholonomic constrain and intrinsical nonlinear nonholonomic constrain are put forward in this paper. The nonholonomic systems are divided into intrinsical linear nonholonomic system and intrinsical nonlinear nonholonomic system.The rational spectrums of all kinds of virtual displacement definitions and commutativity of d, ?operations are given and testified in this paper. The research methods of intrinsical linear nonholonomic dynamics are similar to those of holonomic dynamics.The rationality and equivalence of Chetaev model and Vacco model in the intrinsical linear nonholonomic system are testified from the mathematic and mechanical aspects. The essential reason is the nonlinear property of intrinsical nonlinear nonholonomic constrain that bring on Chetaev model and Vacco model inequivalent. Chetaev model is a linear approximate method in intrinsical nonlinear nonholonomic system. Vacco dynamical equations are not satisfied to the ideal constraint force conditions, but it gives a significative ponderation on the realizations of intrinsical nonlinear nonholonomic constrain. A new and rational method must be given to deal with intrinsical nonlinear nonholonomic dynamics.Hamilton principle can be used in holonomic system and intrinsical linear nonholnomic system. The formulas of them are unified. Hamiltonian action is stability in intrinsical linear nonholnomic system.