Investigation of Nonholonomic Mechanics, Vakonomic Mechanics and Chetaev Method in Modeling Constrained Dynamic Systems

In this article, methods of modeling dynamic systems namely, Nonholonomic mechanics, Vakonomic mechanics and Chetaev methods for constrained dynamic system are investigated. The fact that Vakonomic mechanics gives a different motion equation to the other methods is verified using a particular example. It is shown that the three methods give the same motion equation for holonomic system. For nonholonomic system, the Vakonomic dynamics gives a different motion equation to the others. Moreover, Chetaev equation is proved without using Chetaev condition. A particular example is provided in verifying that Chetaev condition is not always valid. Finally, the reason why the Vakonomic mechanics gives a different motion equation in the case of nonholonomic system is scrutinized based on the definition of Vakonomic mechanics whose motion equation is obtained through a purely variational principle. An example is given to strengthen the arguments. Key Terms : Nonholonomic mechanics, Vakonomic mechanics, Chetaev formula, holonomic constraint, semi-holonomic constraints, nonholonomic constraints, Variational principles, Infinitesimal variations