Lie symmetries and conserved quantities for generalized Birkhoff system

To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A conserved quantity of Hojman’s type and a Noether’s conserved quantity are deduced by the Lie symmetry under some conditions. One example is given to illustrate the application of the result.