相对论Birkhoff系统的Noether理论

THE NOETHER′S THEORY OF RELATIVISTIC BIRKHOFF SYSTEMS

给出相对论Pfaff -Birkhoff原理和相对论Birkhoff方程 .定义相对论Birkhoff系统的无限小变换生成元 ,根据在无限小变换下微分变分原理的不变性 ,得到相对论Birkhoff系统的Noether定理和Noether逆定理 .

The Pfaff Birkhoff principle and the Birkhoff equation for relativistic Birkhoff system are derived. By introducing an infinitesimal generator for the relativistic Birkhoff system and based on the invariance of the differentiation variation principle under the infinitesimal transformations,the Noether theorem and Noether inverse theorem of the relativistic Birkhoff system are obtained. An example is given to show the applicability of the theorems.