A General Approach to the Construction of Conservation Laws for Birkhoffian Systems in Event Space

摘要

For a Birkhoman system in the event space,a general approach to the construction of conservation lawsis presented.The conservation laws are constructed by finding corresponding integrating factors for the parametricequations of the system.First,the parametric equations of the Birkhoffian system in the event space are established,and the definition of integrating factors for the system is given;second the necessary conditions for the existence ofconservation laws are studied in detail,and the relation between the conservation laws and the integrating factors ofthe system is obtained and the generalized Killing equations for the determination of the integrating factors are given;finally,the conservation theorem and its inverse for the system are established,and an example is given to illustrate theapplication of the results.