分析力学中Santilli方法和Engels第一方法的意义和局限性  

SIGNIFICANCE AND LIMITATIONS OF SANTILLI' METHOD AND FIRST ENGELS' METHOD IN ANALYTICAL MECHANICS

作　　者：丁光涛[1] DING Guangtao(College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, Anhui, China)

机构地区：[1]安徽师范大学物理与电子信息学院,安徽芜湖241000

出　　处：《力学与实践》2017年第2期180-184,共5页Mechanics in Engineering

基　　金：国家自然科学基金资助项目(11472063)

摘　　要：讨论变分法逆问题理论中的两种构造拉格朗日函数的基本方法:Santilli方法和Engels第一方法.(1)指出Santilli方法的理论意义在于直接用构造法证明自伴随微分方程能够从变分原理导出,即表示为欧勒-拉格朗日方程形式.(2)提出利用Santilli方法构造的结果,不是唯一的拉格朗日函数,而是一规范等效的拉格朗日函数族,为此修正了该方法.(3)指出在实际应用中Santilli方法的局限性,特别是对某些力学系统,可能因对参变量的定积分发散,而不能有效构造拉格朗日函数.(4)分析Engels第一方法的意义和优越性,同时指出这种方法存在与Santilli方法相似的局限性.(5)以两个力学系统为例,说明上述讨论的结论.Two methods for the construction of a Lagrangian in the theory of inverse problem,the Santilli’method and theˉrst Engels’method,are discussed.(1)It is pointed out that the theoretical signiˉcance of the Santilli'method is in the fact that by a direct construction of Lagrangian one may prove that the self-adjoint differential equations can be derived by the variational principle,that is,represented in terms of the Lagrange's equations.(2)It is manifested that what constructed by the Santilli'method is not a unique Lagrangian,buta family of gauge equivalent Lagrangians,and the Santilli'method is modiˉed.(3)The defects of the Santilli'method in practical applications are pointed out,especially for some mechanical systems,because the deˉniteintegral depending on a parameter is divergent,so the Lagrangian can not be constructed.(4)The signiˉcance and advantages of theˉrst Engels'method are discussed,and the defects of this method are also pointed out.(5)Two examples are given to illustrate the application of the result.

关 键 词：逆问题 拉格朗日函数 Santilli方法 Engels第一方法 

分 类 号：O316[理学—一般力学与力学基础]