[1]王嘉航,张 毅.约束广义Birkhoff系统的运动稳定性[J].江西师范大学学报(自然科学版),2017,(02):212-214.
　WANG Jiahang,ZHANG Yi.The Stability of Motion for the Generalized Birkhoffian System with Constrains[J].Journal of Jiangxi Normal University:Natural Science Edition,2017,(02):212-214.
点击复制

约束广义Birkhoff系统的运动稳定性()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2017年02期
页码:
212-214
栏目:
出版日期:
2017-03-01

文章信息/Info

Title:
The Stability of Motion for the Generalized Birkhoffian System with Constrains
作者:
王嘉航; 张 毅
1.苏州科技大学土木工程学院,江苏 苏州 215011; 2.河海大学土木与交通学院,江苏 南京 210098
Author(s):
WANG Jiahang; ZHANG Yi
1.College of Civil Engineering,Suzhou University of Science and Technology,Suzhou Jiangsu 215011,China; 2.College of Civil and Transportation Engineering,Hohai University,Nanjing Jiangsu 210098,China
关键词:
广义Birkhoff系统;  运动稳定性;  1次近似法;  直接法
Keywords:
generalized Birkhoffian system;  stability of motion;  first approximation theory;  direct method
分类号:
O 316
文献标志码:
A
摘要:
利用Noether理论对约束广义Birkhoff系统的稳定性问题进行了研究,给出了约束广义Birkhoff系统的受扰运动方程; 得到了约束广义Birkhoff系统的1次近似方程,利用Lyapnnov 1次近似理论,建立了约束广义Birkhoff系统稳定性的判据; 利用Noether守恒量构造Lyapnnov函数,建立了直接法的系统平衡状态稳定性的判据,并举例说明它的应用.
Abstract:
The problem on the stability of motion for a generalized Birkhoffian system with constrains are studied by the Noether theong.The disturbed equations of motion and their first approximation for the system are established.The criterion of stability of motion for the system was set up by using Lyapnnov’s first approximation theory.The Lyapnnov’s function was constructed by the Noether conserved quantity and the criterion of stability of motion for the system was also set up by using Lyapnnov’s direct method.Finally,the example is given to illustrate the application of the results.

参考文献/References:

[1] 梅凤翔,史荣昌,张永发,等.约束力学系统的运动稳定性 [M].北京:北京理工大学出版社,1997:33-290.
[2] 梅凤翔.广义Birkhoff系统动力学 [M].北京:科学出版社2013:65-203.
[3] 梅凤翔.关于受约束Birkhoff系统的平衡稳定性 [J].北京理工大学学报:自然科学版,1996(3):242-250.
[4] Zhang Yi.Stability of motion for generalized Birkhoffian systems [J].J China Ordnance,2010,6(3):161-165.
[5] 曹秋鹏,张毅,陈向炜.约束自治广义Birkhoff系统平衡稳定性的梯度系统方法 [J].云南大学学报:自然科学版,2015,37(2):228-232.
[6] 金世欣,张毅.受约束的自治广义Birkhoff系统的平衡稳定性 [J].扬州大学学报:自然科学版,2013,16(2):21-25.
[7] 王嘉航,张毅.受约束的广义Birkhoff系统平衡稳定性 [J].苏州科技学院学报,2014,31(4):10-14.
[8] 崔金超,梅凤翔.广义Birkhoff系统的平衡稳定性 [J].动力学与控制学报,2010,8(4):297-299.
[9] Sanchez D A.Ordinary differential equations and stability theory:an introduction [M].New York:Dover Publications Inc,2012:91-117.
[10] 张毅.自治广义Birkhoff系统的平衡稳定性 [J].物理学报,2010,59(1):20-25.
[11] Li Yanmin,Mei Fengxiang.Stability for manifolds of equilibrium states of generalized Birkhoff system [J].Chin Phys B,2010,19(8):1-3.
[12] Mei Fengxiang,Wu Huibin.Form invariance and new conserved quantity of generalized Birkhoffian system [J].Chin Phys B,2010,19(5):1-4.
[13] Jiang Wenan,Luo Shaokai.Stability for manifolds of equilibrium states of generalized Hamiltonian system [J].Meccanica,2012,47(2):379-383.
[14] Mei Fengxiang,Wu Huibin,Shang Mei.Stability with respect to partial variables for Birkhoffian system [J].Chin Phys B,2006,15(9):1932-1934.
[15] Mei Fengxiang,Xie Jiafang,Gang Tieqiang.Stability of motion of a nonholonomic system [J].Chin Phys Lett,2007,24(5):1133-1135.

备注/Memo

备注/Memo:
收稿日期:2016-12-26基金项目:国家自然科学基金(10972151,11272227)资助项目.通信作者:张 毅(1964-),男,江苏吴江人,教授,博士生导师,主要从事数学物理方程的研究.E-mail:weidiezh@gmail.com
更新日期/Last Update: 1900-01-01