Manifold stability of equilibrium state of autonomous generalized Birkhoff system

Abstract

摘要 研究广义Birkhoff自治系统平衡状态流形稳定性. 建立广义Birkhoff自治系统的受绕运动方程和平衡方程. 由Liapunov稳定性理论给出广义Birkhoff自治系统的平衡状态流形稳定性的有关判据. 举例说明结果的应用. 关键词: 广义Birkhoff方程 / 自治系统 / 平衡状态 / 流形稳定性 Abstract Manifold stability of equilibrium state of autonomous generalized Birkhoff system is studied. The perturbation equation and equilibrium equation of autonomous generalized Birkhoff system is established. The corresponding criteria for manifold stability of autonomous generalized Birkhoff system is given by the Liapunov stability theory. Finally, an example is presented to illustrate these results. Keywords: generalized Birkhoff system / autonomous system / equilibrium state / manifold stability 作者及机构信息 李广成, 陈雷明, 王东晓, 武大勇 1. 郑州航空工业管理学院数理系,郑州 450015 基金项目: 国家自然科学基金（批准号:10772026）和河南省教育厅自然科学基金（批准号:2008A130002, 2008A140013）资助的课题. Authors and contacts Li Guang-Cheng, Chen Lei-Ming, Wang Dong-Xiao, Wu Da-Yong 1. 郑州航空工业管理学院数理系,郑州 450015 参考文献 [1] ［1］Birkhoff G D 1927 Dynamical systems (Providence RI: AMS College Publ) [2] ［2］Stantilli R M 1983 Foundations of theoretical mechanics Ⅱ (New York: Spring-Verlag) [3] ［3］Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian System (Beijing: Beijing Institute of Technology Press) (in Chinese) ［梅凤翔、史荣昌、张永发、吴惠彬 1996 Birkhoff系统动力学 （北京：北京理工大学出版社）］ [4] ［4］Mei F X 1993 Chin. Sci. Bull. 38 311(in Chinese) ［梅凤翔 1993 科学通报 38 311］ [5] ［5］Mei F X 1997 Journal of Beijing Institute of Technology 6 106 (in Chinese) ［梅凤翔 2000北京理工大学学报6 106］ [6] ［6］Luo S K 2002 Acta Phys. Sin. 51 1416 (in Chinese) ［罗绍凯2002 物理学报 51 1416］ [7] ［7］Mei F X 1993 Science in China A 36 1456 ［梅凤翔 1993 中国科学 A 36 1456］ [8] ［8］Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4658.(in Chinese) ［梅凤翔、蔡建乐 2008 物理学报 57 4658］ [9] ［9］Mei F X, Xie J F, Gang T Q 2008 Acta Phys. Sin. 57 4649 (in Chinese) ［梅凤翔、解加芳、冮铁强2008物理学报57 4649］ [10] ］Chen X W, Mei F X 2000 Journal of Beijing Institute of Technology 9 5 (in Chinese) ［陈向炜、梅凤翔 2000北京理工大学学报9 5］ [11] ］Chen X W, Fu J L, Luo, S K 2000 Jour. Shangqiu Tech. Coll. 16 6(in Chinese) ［陈向炜、付景礼、罗绍凯2000商丘师院学报16 6］ [12] ］Mei F X, Shi R C, Zhang Y F, Zhu H P 1996 Stability of the Constrained Mechanics System (Beijing: Beijing Institute of Technology Press) (in Chinese) ［梅凤翔、史荣昌、张永发、朱海平 1996 约束力学系统的运动稳定性 （北京：北京理工大学出版社）］ 施引文献