构造Birkhoff函数(组)的参数调节法  

Parameter-Adjusting Method of Constructing Birkhoffian Functions

作　　者：宋端[1] 刘畅[2] 郭永新[2,3] 

机构地区：[1]辽东学院影像物理教研室,辽宁丹东118001 [2]辽宁大学物理学院,沈阳110036 [3]辽东学院机电工程系,辽宁丹东118001

出　　处：《应用数学和力学》2013年第9期995-1002,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11172120;90;932002)~~

摘　　要：根据偏微分方程的Cauchy-Kovalevski可积性定理,将欠定的Birkhoff方程组转化为以Birk-hoff函数组为未知变量的完备的偏微分方程组,提出了构造Birkhoff动力学函数的参数调节法.通过调节补偿方程中的两类可调的函数参数就能得到不同的Birkhoff函数组.并把构造Birkhoff函数组的参数调节法与Santilli构造方法进行了比较,例如研究了利用动力学系统独立的第一积分构造Birkhoff函数组的Hojman方法与参数调节法之间的关系.最后,给出应用实例验证了参数调节法的实用性及其与Santilli 3种构造方法的关系.The parameter-adjusting method to construct dynamical functions of Birkhoff＇ s e- quations is put forward based on realizing the completeness of Birkhoff＇ s equations, which are under-determinate, by means of Cauchy-Kovalevski integrability theorem for partial differential equations. The two kinds of parameters in the compensatory equation were capable of adjusting to get different sets of Birkhoffian functions. The existing methods, such as Hojman＇ s method using 2n first integrals for dynamical systems with symmetry, were compared with the parame- ter-adjusting method. Finally, The compensatory equation for the Birkhoff＇ s equations can be simplified by means of some limitations on the two kinds of parameters, where the relation be- tween the Birkhoffian functions and parameters become more evident.

关 键 词：BIRKHOFF方程 Cauchy—Kovalevski定理 自伴随微分方程 参数调节法 

分 类 号：O316[理学—一般力学与力学基础]