小参数摄动法与保辛  

SMALL PARAMETER PERTURBATION METHOD AND SYMPLECTIC CONSERVATION

作　　者：钟万勰[1] 孙雁[2] 

机构地区：[1]大连理工大学工程力学系,大连116023 [2]上海交通大学工程力学系,上海200030

出　　处：《动力学与控制学报》2005年第1期1-6,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金(10372019);教育部博士点基金资助项目(20010141024)~~

摘　　要：应用数学与力学经常使用小参数摄动近似.在物理与力学中有大量保守体系的分析.保守体系的特点是保辛.本文指出小参数摄动法保辛的问题应予考虑.位移法摄动是保辛的,而辛矩阵的加法摄动则未能保辛.数值例题给出了对比.The small parameter perturbation approximation is applied quite often in applied mathematics and mechanics. There are tremendous conservative system analyses in physics and applied mechanics, and one of the most important characteristics of a conservative system is its symplectic conservation. The present paper emphasizes that the symplectic conservative behavior should be considered in small parameter perturbation approximations. The strip domain structural analysis is considered, and we gave both the perturbation solutions with the displacement method, which is symplectic conservative, and the perturbation solutions with the corresponding transfer symplectic matrix method, which is symplectic non-conservative.

关 键 词：小参数摄动法 应用数学 位移法 辛矩阵 力学 近似 加法 

分 类 号：O342[理学—固体力学]