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A gradient representation of the first-order Lagrange system is studied. A condition under which the first-order Lagrange system can be considered as a gradient system is obtained. The stability of the system is discussed by using the property of the gradient system. Some examples are given to illustrate the application of the result.
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Keywords:
- first-order Lagrange system /
- gradient system /
- stability
[1] Santilli R M 1978 Foundations of Theoretical Mechanics I (New York: Springer-Verlag)
[2] Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1896
[3] Ding G T, Tao S T 2008 Chin. Sci. Bull. 53 872 (in Chinese) [丁光涛, 陶松涛 2008 科学通报 53 872]
[4] Li Z P 1993 Classical and Quantal Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing: Beijing University of Technology Press) (in Chinese) [李子平 1993 经典和量子约束系统及其对称性质 (北京: 北京工业大学出版社)]
[5] Mei F X, Zhu H P 2000 J. of Beijing Institute of Technology 9 11
[6] Ge W K, Mei F X 2001 J. of China Ordnance 22 241 (in Chinese) [葛伟宽, 梅凤翔 2001 兵工学报 22 241]
[7] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) [梅凤翔, 尚玫 2000 49 1901]
[8] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔 2004 约束力学系统的对称性与守恒量 (北京: 北京理工大学出版社)]
[9] Chen X W, Shang M, Mei F X 2001 Chin. Phys. 10 997
[10] Chen X W, Liu C, Mei F X 2008 Chin. Phys. B 17 3180
[11] Liu C, Zhu N, Mei F X, Guo Y X 2008 Communications in Theoretical Physics 50 1065
[12] Hirsch M W, Smale S, Devaney R L 2008 Differential Equation, Dynamical Systems and an Introduction to Chaos (Singapore: Elsevier)
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[1] Santilli R M 1978 Foundations of Theoretical Mechanics I (New York: Springer-Verlag)
[2] Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1896
[3] Ding G T, Tao S T 2008 Chin. Sci. Bull. 53 872 (in Chinese) [丁光涛, 陶松涛 2008 科学通报 53 872]
[4] Li Z P 1993 Classical and Quantal Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing: Beijing University of Technology Press) (in Chinese) [李子平 1993 经典和量子约束系统及其对称性质 (北京: 北京工业大学出版社)]
[5] Mei F X, Zhu H P 2000 J. of Beijing Institute of Technology 9 11
[6] Ge W K, Mei F X 2001 J. of China Ordnance 22 241 (in Chinese) [葛伟宽, 梅凤翔 2001 兵工学报 22 241]
[7] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) [梅凤翔, 尚玫 2000 49 1901]
[8] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔 2004 约束力学系统的对称性与守恒量 (北京: 北京理工大学出版社)]
[9] Chen X W, Shang M, Mei F X 2001 Chin. Phys. 10 997
[10] Chen X W, Liu C, Mei F X 2008 Chin. Phys. B 17 3180
[11] Liu C, Zhu N, Mei F X, Guo Y X 2008 Communications in Theoretical Physics 50 1065
[12] Hirsch M W, Smale S, Devaney R L 2008 Differential Equation, Dynamical Systems and an Introduction to Chaos (Singapore: Elsevier)
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