Noether—Birkhoff动力学逆问题

研究新型的Birkhoff系统动力学逆问题，利用Noether理论直接从已知的系统第一积分构建系统的Birkhoff函数B和Birkhoff函数组Ru，并且同时导出与第一积分作为Noether守恒量相对应的对称变换生成元和规范函数．给出这类动力学逆问题的提法和3种解法，并对3种特殊情况得到3个推论．讨论解的集合中不同解的等效性．举例说明所得结果的应用．

Noether-Birkhoff inverse problem of dynamics

A New type of inverse problems of dynamics for a Birkhoffian systerm is studied. By using Noether＇s theory the Birkhoffian and Birkhoffian functions of a systerm are constructed directly from the known first integrals of the systerm, and the generators and the gauge functions of symmetrics transformations corresponding to the first integrals as the conserved quantities are deduced simultaneously. A formulation and three solutions for this type of inverse problems are presented, and three corollaries for three special cases are obtained. The equivalence relation of the different solutions in the set of solutions is discussed. An example is given to illustrate the application of the results.