Mei symmetry and conserved quantity of a Birkhoffian system in event space

To further reveal the inner relationships between symmetries and conserved quantities,the Mei symmetry and the conserved quantity of a Birkhoffian system in event space are studied here.Firstly,the parameter equations of the Birkhoffian system in event space are established;next,based on the invariance that the dynamical functions in the parameter equations still satisfy the equations after undergoing the infinitesimal transformations,the definition of Mei symmetry and the criterion equation of the Birkhoffiian system in event space are given;finally,the conserved quantity deduced by the symmetry is obtained and two examples are given to illustrate the application of the results.The methods and results of this paper may be further developed to other constrained mechanical systems in event space.