Bessel方程的Noether对称性和守恒量  

On noether symmetries and conserved quantities of Bessel equation

作　　者：姜文安[1] 孙鹏 谷家杨 夏丽莉 JIANG Wen-an;SUN Peng;GU Jia-yang;XIA Li-li(School of Naval Architecture and Ocean Engineering,Jiangsu University of Science and Technology, Zhenjiang 212003, China;School of Applied Science, Beijing Information Science and Technology University,Beijing 100192, China)

机构地区：[1]江苏科技大学船舶与海洋工程学院,江苏镇江212003 [2]北京信息科技大学理学院,北京100192

出　　处：《云南大学学报（自然科学版）》2018年第4期697-704,共8页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11702119;51779109;11502071);江苏省自然科学基金(BK20170565)

摘　　要：Birkhoff力学比Hamilton力学更普遍,但只有一些动力系统能够实现Birkhoff化.文章基于Santilli的第一方法,给出经典贝塞尔方程的一种新型Birkhoff化.通过引入Lie群无穷小变换下的不变性,建立Bessel方程的Noether对称性变换与准对称性变换,给出相应的对称性判据.得到Bessel方程Noether定理导致的守恒量,以及Noether逆定理.最后,给出n阶经典Bessel方程的Noether定理导致的一个守恒量,说明本方法的有效性.The Birkhoffan mechanics is more general than the Hamilton systems, but only for some dynamical systems can be applied by a Birkhoffan formulations.This paper explores a novel Birkhoffan formulations of the classical Bessel equation.Based on the first method of Santilli ,Birkhoffan formulation of Bessel equation has been established.The Noether symmetric and quasisymmetric transformations of the Bessel equation have been established by introducing the invariance of the action under infinitesimal transformations, the criteria of corresponding symmetries are proposed.The Noether theorems of Bessel equation have been presented, and the conserved quantities have been obtained and n-th order classical Bessel equation has been studied to show the effectiveness of the proposed method.

关 键 词：Birkhoffian化 NOETHER对称性 守恒量 BESSEL方程 

分 类 号：O316[理学—一般力学与力学基础]