Abstract: The article argues that defining virtual displacement as the difference of two possible displacements is more general. In this way, one can not only obtain the same commutative properties of derivative and variational operations and the commutative properties of integral and variational operations, but also obtain the Hamiltons principle. More importantly, one can study the virtual perturbations of more types of constrained systems and different types of virtual perturbations occurring in the same constrained system, so as to derive the equations satisfied by the generalized virtual displacements of the system. Meanwhile, for a general firstorder nonholonomic constrained system, whether it is subjected to a Jourdain virtual perturbation or a Gauss virtual perturbation, the Chetaev relation can be derived. The relation satisfied by the generalized virtual displacement of a firstorder linear constrained system is simply a special case of the Chetaev relation.

Key words: possible infinitesimal perturbation, possible displacement, virtual displacement, Jourdain virtual perturbation, Gauss virtual perturbation, Chetaev relation, Hamiltons principle