Please wait a minute...
Chinese Physics, 2006, Vol. 15(8): 1669-1671    DOI: 10.1088/1009-1963/15/8/004
GENERAL Prev   Next  

An inverse problem in analytical dynamics

Li Guang-Cheng(李广成) and Mei-Feng-Xiang(梅凤翔)
Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
Abstract  This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.
Keywords:  inverse problem      analytical dynamics      integral      Lagrangian  
Received:  30 December 2005      Revised:  16 February 2005      Accepted manuscript online: 
PACS:  02.30.Zz (Inverse problems)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10272021, 10572021) and the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022).

Cite this article: 

Li Guang-Cheng(李广成) and Mei-Feng-Xiang(梅凤翔) An inverse problem in analytical dynamics 2006 Chinese Physics 15 1669

[1] Measuring stellar populations, dust attenuation and ionized gas at kpc scales in 10010 nearby galaxies using the integral field spectroscopy from MaNGA
Niu Li(李牛) and Cheng Li(李成). Chin. Phys. B, 2023, 32(3): 039801.
[2] State-to-state integral cross sections and rate constants for the N+(3P)+HD→NH+/ND++D/H reaction: Accurate quantum dynamics studies
Hanghang Chen(陈航航), Zijiang Yang(杨紫江), and Maodu Chen(陈茂笃). Chin. Phys. B, 2022, 31(9): 098204.
[3] Bandwidth expansion and pulse shape optimized for 10 PW laser design via spectral shaping
Da-Wei Li(李大为), Tao Wang(王韬), Xiao-Lei Yin(尹晓蕾), Li Wang(王利), Jia-Mei Li(李佳美),Hui Yu(余惠), Yong Cui(崔勇), Tian-Xiong Zhang(张天雄), Xing-Qiang Lu(卢兴强), and Guang Xu(徐光). Chin. Phys. B, 2022, 31(9): 094210.
[4] Integral cross sections for electron impact excitations of argon and carbon dioxide
Shu-Xing Wang(汪书兴) and Lin-Fan Zhu(朱林繁). Chin. Phys. B, 2022, 31(8): 083401.
[5] A new global potential energy surface of the ground state of SiH2+ (X2A1) system and dynamics calculations of the Si+ + H2 (v0 = 2, j0 = 0) → SiH+ + H reaction
Yong Zhang(张勇), Xiugang Guo(郭秀刚), and Haigang Yang(杨海刚). Chin. Phys. B, 2022, 31(11): 113101.
[6] Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube
Haiyan Lin(林海燕), Yang Xiang(向阳, Hong Liu(刘洪), and Bin Zhang(张斌). Chin. Phys. B, 2021, 30(3): 030501.
[7] Stabilization strategy of a car-following model with multiple time delays of the drivers
Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2021, 30(12): 120506.
[8] Exact quantum dynamics study of the H(2S)+SiH+(X1Σ+) reaction on a new potential energy surface of SiH2+(X2A1)
Wen-Li Zhao(赵文丽), Rui-Shan Tan(谭瑞山), Xue-Cheng Cao(曹学成), Feng Gao(高峰), and Qing-Tian Meng(孟庆田). Chin. Phys. B, 2021, 30(12): 123403.
[9] Mechanism analysis of reaction S+(2D)+H2(X1Σg+)→SH+(X3Σ-)+H(2S) based on the quantum state-to-state dynamics
Jin-Yu Zhang(张金玉), Ting Xu(许婷), Zhi-Wei Ge(葛志伟), Juan Zhao(赵娟), Shou-Bao Gao(高守宝), Qing-Tian Meng(孟庆田). Chin. Phys. B, 2020, 29(6): 063101.
[10] Influence of the Earth's rotation on measurement of gravitational constant G with the time-of-swing method
Jie Luo(罗杰), Tao Dong(董涛), Cheng-Gang Shao(邵成刚), Yu-Jie Tan(谈玉杰), Hui-Jie Zhang(张惠捷). Chin. Phys. B, 2020, 29(2): 020401.
[11] Non-adiabatic quantum dynamical studies of Na(3p)+HD(ν=1, j=0)→NaH/NaD+D/H reaction
Yue-Pei Wen(温月佩), Bayaer Buren(布仁巴雅尔), Mao-Du Chen(陈茂笃). Chin. Phys. B, 2019, 28(6): 063401.
[12] Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems
Li-Li Xia(夏丽莉), Xin-Sheng Ge(戈新生), Li-Qun Chen(陈立群). Chin. Phys. B, 2019, 28(3): 030201.
[13] Dynamics of the Au+H2 reaction by time-dependent wave packet and quasi-classical trajectory methods
Yong Zhang(张勇), Chengguo Jiang(姜成果). Chin. Phys. B, 2019, 28(12): 123101.
[14] Second-order interference of two independent photons with different spectra
Yu Zhou(周宇), Jian-Bin Liu(刘建彬), Huai-Bin Zheng(郑淮斌), Hui Chen(陈辉), Fu-Li Li(李福利), Zhuo Xu(徐卓). Chin. Phys. B, 2019, 28(10): 104205.
[15] Derivation of lattice Boltzmann equation via analytical characteristic integral
Huanfeng Ye(叶欢锋), Bo Kuang(匡波), Yanhua Yang(杨燕华). Chin. Phys. B, 2019, 28(1): 014701.
No Suggested Reading articles found!