  Dynamical systems, described by Lagrangians with first- and second-class
constraints, are investigated. In the Dirac approach to the generalized
Hamiltonian formalism, the classification and separation of the first- and
second-class constraints are presented with the help of passing to an
equivalent canonical set of constraints. The general structure of second-class
constraints is clarified. The method of constructing the generator of symmetry
transformations in the second Noether theorem is given. It is proved that
second-class constraints do not contribute to the transformation law of the
local symmetry which entirely is entirely stipulated by all the first-class
constraints.
