| Abstract: | The Noether symmetries and the conserved quantities for generalized Birkhoffian systems with time delay are studied.Firstly,the generalized Pfaff-Birkhoff principle with time delay is proposed,and the generalized Birkhoff's equations with time delay are obtained.Secondly,the generalized Noether quasi-symmetric transformations of the system are defined,and the criterion of the Noether symmetries is established.Then the Noether theorem for generalized Birkhoffian systems with time delay is established.Finally,by imposing restrictions of constraints on the infinitesimal transformations,the Noether theorem of constrained Birkhoffian systems with time delay is established.One example is given to illustrate the application of the results. |
