Form Invariance and Lie Symmetry of Constrained Birkhoffian Systems

Relation between the form invariance and Lie symmetry of constrained Birkhoffian systems is studied. First, the definitions and criterions of the form invariance and Lie symmetry in the systems are given. Next, the relation between them is expounded and proved. It is shown that the structure equation and conserved quantity of the form invariance and Lie symmetry of constrained Birkhoffian systems have the same form. Finally, an example is given to illustrate the application of the result.