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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.
[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）］
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[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）］
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