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中文摘要：
为了进一步揭示对称性与守恒量的内在关系,作者研究了事件空间中Birkhoff系统的Mei对称性与守恒量.首先,建立事件空间中Birkhoff系统的参数方程;其次,基于该参数方程中出现的动力学函数在经历无限小变换后仍然满足原方程的一种不变性,给出事件空间中Birkhoff系统Mei对称性的定义和确定方程;最后,得到由Mei对称性导出的守恒量并举例说明结果的应用.该文研究方法和结果可进一步拓展到事件空间中其它约束力学系统.
英文摘要：
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.
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