非线性非保守系统的近似Birkhoffian化  

Approximate Birkhoffian formulations for nonlinear nonconservative systems

作　　者：姜文安[1] 夏丽莉 JIANG Wenan;XIA Lili(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,镇江212003 [2]北京信息科技大学理学院,北京100192

出　　处：《江苏科技大学学报（自然科学版）》2019年第1期121-123,130,共4页Journal of Jiangsu University of Science and Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(11702119;11502071);江苏省自然科学基金资助项目(BK20170565)

摘　　要：研究了非线性非保守动力学系统的近似Birkhoffian化.基于等效线性化方法,通过平方误差累积最优原理,给出了非线性非保守系统的等效线性化系统.运用Santilli第一方法,得到Birkhoff函数为系统总能量的近似Birkhoff系统.最后,应用文中提出的方法,给出了两类非线性非保守系统的近似Birkhoffian方程.This paper develops a novel approximate Birkhoffian analytical expression for nonlinear nonconservative systems. Based on the method of equivalent linearization, equivalent linear system is derived from minimizing the squared of the error. Birkhoffian equation is established in which the Birkhoffian function describes the total physical energy of the corresponding conservative systems. Finally, two different examples are studied to show the application of the proposed method.

关 键 词：非保守系统 Birkhoffian化 等效线性化方法 

分 类 号：O324[理学—一般力学与力学基础]