Generalized Noether theorems and applications (Q1174414)

A mechanical system with \(N\) degrees of freedom is investigated provided that it is described by a singular Lagrangian \(L(t,q,\dot q)\), \(q=(q^ 1,\dots,q^ N)\). The system considered is subjected to the constraints \(G_ k(q,p)=0\), \(k=1,\dots,K\), where \(p=(p_ 1,\dots,p_ n)\) are the generalized moments corresponding to the generalized coordinates \(q\). For such a system the first Noether theorem is generalized. An example is given for which the Dirac conjecture fails. The second problem studied concerns the transformation properties of the system under an infinite continuous group in terms of canonical variables. In this way generalized Noether identities are obtained. These identities are applied to nonrelativistic charged particles in an electromagnetic field on the constrained hypersurface. The paper reads well.