An inverse problem in analytical dynamics

doi:10.1088/1009-1963/15/8/004

中国物理B ›› 2006, Vol. 15 ›› Issue (8): 1669-1671.doi: 10.1088/1009-1963/15/8/004

An inverse problem in analytical dynamics

李广成, 梅凤翔

Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2005-12-30 修回日期:2005-02-16 出版日期:2006-08-20 发布日期:2006-08-20
基金资助:
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).

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

Received:2005-12-30 Revised:2005-02-16 Online:2006-08-20 Published:2006-08-20
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: inverse problem, analytical dynamics, integral, Lagrangian

中图分类号: (Inverse problems)

02.30.Zz

45.20.Jj (Lagrangian and Hamiltonian mechanics) 02.30.Jr (Partial differential equations)

李广成, 梅凤翔. An inverse problem in analytical dynamics[J]. 中国物理B, 2006, 15(8): 1669-1671.

Li Guang-Cheng(李广成) and Mei-Feng-Xiang(梅凤翔). An inverse problem in analytical dynamics[J]. Chinese Physics, 2006, 15(8): 1669-1671.

[1]	Yong Huang(黄勇) and Yang Li(李扬). Data-driven modeling of a four-dimensional stochastic projectile system[J]. 中国物理B, 2022, 31(7): 70501-070501.
[2]	Bi-Chun Dong(董必春), Run-Mei Zhang(张润梅), Bin Yuan(袁彬), and Chuan-Yang Yu(俞传阳). Nearfield acoustic holography in a moving medium based on particle velocity input using nonsingular propagator[J]. 中国物理B, 2022, 31(2): 24303-024303.
[3]	. [J]. 中国物理B, 2021, 30(3): 30203-.
[4]	汪洋, 赵小峰. Theoretical framework for geoacoustic inversion by adjoint method[J]. 中国物理B, 2019, 28(10): 104301-104301.
[5]	秦雪. Factorization method for inverse obstacle scattering problem in three-dimensional planar acoustic waveguides[J]. 中国物理B, 2018, 27(10): 100203-100203.
[6]	陈琳, 郑志伟, 包立君, 方金生, 杨天和, 蔡淑惠, 蔡聪波. Weighted total variation using split Bregman fast quantitative susceptibility mapping reconstruction method[J]. 中国物理B, 2018, 27(8): 88701-088701.
[7]	刘冠楠, 刘冬. Reconstruction model for temperature and concentration profiles of soot and metal-oxide nanoparticles in a nanofluid fuel flame by using a CCD camera[J]. 中国物理B, 2018, 27(5): 54401-054401.
[8]	徐征, 李想, 郭盼, 吴嘉敏. Equivalent magnetic dipole method used to design gradient coil for unilateral magnetic resonance imaging[J]. 中国物理B, 2018, 27(5): 58702-058702.
[9]	乔要宾, 齐宏, 赵方舟, 阮立明. Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation[J]. 中国物理B, 2016, 25(12): 120201-120201.
[10]	皇群博, 曹小群, 朱孟斌, 张卫民, 刘柏年. New data assimilation system DNDAS for high-dimensional models[J]. 中国物理B, 2016, 25(5): 50502-050502.
[11]	牛春洋, 齐宏, 任亚涛, 阮立明. Apparent directional spectral emissivity determination of semitransparent materials[J]. 中国物理B, 2016, 25(4): 47801-047801.
[12]	文方青, 张弓, 贲德. Direction-of-arrival estimation for co-located multiple-input multiple-output radar using structural sparsity Bayesian learning[J]. 中国物理B, 2015, 24(11): 110201-110201.
[13]	陈兴乐, 雷银照. Inverse problem of pulsed eddy current field of ferromagnetic plates[J]. , 2015, 24(3): 30301-030301.
[14]	颜冰, 黄思训. Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction[J]. , 2014, 23(10): 109402-109402.
[15]	王龙庆, 王为民. Multi-objective optimization of gradient coil for benchtop magnetic resonance imaging system with high-resolution[J]. 中国物理B, 2014, 23(2): 28703-028703.

An inverse problem in analytical dynamics

An inverse problem in analytical dynamics

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0