Poincare was propounding the fruitful idea to present the equations for holonomic stationary systems in independent variables. Besides some transitive Li group of infinitesimal transformations was used. Chetayev was developing this idea to the non-stationary constraints case, and also to the case of dependent variables, if Li group is intransitive. Besides Chetayev noted, that Poincare equations have the sense also for the closed system of the transformations, for that structural coefficients may be changeable ones. But Poincare and Chetayev were considering in this only the case of constant coefficients. Chetayev was introducing important concept of cyclic variables; he was transforming Poincare equations to the canonic form, and he was developing the theory integrating these equations.
Poincare and Chetayev equations, based on closed systems of transformation, is named the generalized Poincare and Chetayev equations. It is proved, that the special cases of these equations are Lagrange an Hamilton equations in dependent variables, and also Boltzmann-Hamel’s equations in quasi-coordinates; Chetayev equations are represent the hamiltonian-type equations in non-canonical variables. The equivalence to the generalized equations Poincare and Chetayev of all known equations of motion both holonomic and non-holonomic systems is shown. This article represent an introduction in the theory of generalized Poincare and Chetayev equations. The examples are given.