基于非标准Lagrange函数的动力学系统的Routh降阶法
Routh Method of Reduction for Dynamic Systems with Non-Standard Lagrangians
查看参考文献22篇
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文摘
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研究基于指数Lagrange函数与Lagrange函数幂函数两种非标准Lagrange函数的动力学系统的循环积分与Routh降阶法.首先,给出了循环坐标的定义,并利用循环坐标与基于非标准Lagrange函数的系统的Lagrange方程,得到了循环积分的形式;其次,将Routh降阶法加以推广,建立了基于非标准Lagrange函数的动力学系统的Routh方程,并举例说明结果的应用. |
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其他语种文摘
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The cyclic integral and Routh method of reduction for the dynamic system based on exponential Lagrangians and power law Lagrangians were studied. Firstly, the cyclic coordinate was defined, and the form of cyclic integral were obtained by using cyclic coordinates and Lagrange equations of the system with non-standard Lagrangians. Then, the Routh method of reduction was extended, the Routh equations for the dynamic system with non-standard Lagrangians were established. Two examples were given to illustrate the application of the results. |
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来源
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力学季刊
,2016,37(1):15-21 【扩展库】
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DOI
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10.15959/j.cnki.0254-0053.2016.01.002
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关键词
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非标准Lagrange函数
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循环积分
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Routh降阶法
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地址
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1.
苏州科技学院数理学院, 江苏, 苏州, 215009
2.
苏州科技学院土木工程学院, 江苏, 苏州, 215011
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-0053 |
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学科
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力学 |
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基金
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国家自然科学基金
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文献收藏号
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CSCD:5674390
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参考文献 共
22
共2页
|
|
1.
Routh E J.
A treatise on the stability of motion,1877
|
CSCD被引
5
次
|
|
|
|
|
2.
刘端. 非完整系统的Routh方法.
科学通报,1988,33(22):1698-1701
|
CSCD被引
6
次
|
|
|
|
|
3.
Luo S K. Cyclic integrals and reduction of rotational relativistic Birkhoffian system.
Chinese Physics,2003,12(2):140-143
|
CSCD被引
17
次
|
|
|
|
|
4.
张毅. Birkhoff系统约化的Routh方法.
物理学报,2008,57(9):5374-5377
|
CSCD被引
6
次
|
|
|
|
|
5.
罗绍凯. 变质量非完整系统相对于非惯性系运动方程的Routh降阶法.
兵工学报,1996,17(2):159-163
|
CSCD被引
3
次
|
|
|
|
|
6.
Zheng G H. First integrals and reduction of the Birkhoffian system.
Journal of Beijing Institute of Technology:English Edition,2001,10(1):17-22
|
CSCD被引
9
次
|
|
|
|
|
7.
罗绍凯. 转动相对论系统动力学的积分理论.
物理学报,2001,50(11):2053-2058
|
CSCD被引
31
次
|
|
|
|
|
8.
梅凤翔.
分析力学:上册,2013:145-148
|
CSCD被引
1
次
|
|
|
|
|
9.
Arnold V I.
Mathematical methods of classical mechanics,1978
|
CSCD被引
60
次
|
|
|
|
|
10.
Aiekseev A I. Classical Yang-Mills field theory with nonstandard Lagrangians.
Theoretical and Mathematical Physics,1984,59(1):372-378
|
CSCD被引
8
次
|
|
|
|
|
11.
Garousi M R. Constraints on Dirac-Born-Infeld type dark energy models from varying alpha.
Physical Review D,2005,71(8):083005
|
CSCD被引
3
次
|
|
|
|
|
12.
Copeland E J. What is needed of a tachyon if it is to be the dark energy?.
Physical Review D,2005,71(4):317-322
|
CSCD被引
1
次
|
|
|
|
|
13.
Carinena J F. Lagrangian formalism for nonlinear second-order Riccati systems:one-dimensional integrability and two-dimensional superintegrability.
Journal of Mathematical Physics,2005,46(6):547-564
|
CSCD被引
5
次
|
|
|
|
|
14.
Musielak Z E. Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients.
Journal of Physics A:Mathematical and Theoretical,2008,41(5):295-302
|
CSCD被引
11
次
|
|
|
|
|
15.
Musielak Z E. General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems.
Chaos, Solitons & Fractals,2009,42(5):2645-2652
|
CSCD被引
8
次
|
|
|
|
|
16.
Cieslinski J L. A direct approach to the construction of standard and non-standard Lagrangians for dissipative-like dynamical systems with variable coefficients.
Journal of Physics A:Mathematical and Theoretical,2010,43(17):1489-1499
|
CSCD被引
8
次
|
|
|
|
|
17.
El-Nabulsi R A. Non-linear dynamics with non-standard Lagrangians.
Qualitative Theory of Dynamical Systems,2013,12(2):273-291
|
CSCD被引
9
次
|
|
|
|
|
18.
Dimitrijevic D D. About non-standard Lagrangians in cosmology.
Proceedings of the Physics Conference TIM-11, 1472(1),2012:41-46
|
CSCD被引
2
次
|
|
|
|
|
19.
El-Nabulsi R A. Non-standard fractional Lagrangians.
Nonlinear Dynamics,2013,74(1/2):381-394
|
CSCD被引
11
次
|
|
|
|
|
20.
El-Nabulsi R A. Nonstandard Lagrangian cosmology.
Journal of Theoretical and Applied Physics,2013,7(1):1-12
|
CSCD被引
4
次
|
|
|
|
|
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