Motion of general nonholonomic systems from the d’Alembert principle via an algebraic method

The aim of this study is to present an alternative way to deduce the equations of motion of general (i. e. also nonlinear) nonholonomic constrained systems starting from the d’Alembert principle and proceeding by an algebraic procedure. The two classical approaches in nonholonomic mechanics – \({\check{\textrm{C}}}\) $\check{\text{C}}$ etaev method and vakonomic method – are treated on equal terms, avoiding integrations or other steps outside algebraic operations. In the second part of the work, we compare our results with the standard forms of the equations of motion associated with the two method and we discuss the role of the transpositional relation and of the commutation rule within the question of equivalence and compatibility of the \({\check{\textrm{C}}}\) $\check{\text{C}}$ etaev and vakonomic methods for general nonholonomic systems.