NOETHER’S THEORY OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (1): 59-66.

NOETHER’S THEORY OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

张毅¹, 梅凤翔²

1. Suzhou Institute of Urban Construction & Environmental Protection, Suzhou 215011, P R China;
2. Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, P R China

收稿日期:1997-12-08 修回日期:1999-06-11 出版日期:2000-01-18 发布日期:2000-01-18
基金资助:
the National Natural Science Foundation of China(19572018);the Doctoral Programme Foundation of Institution of Higher Education of China

NOETHER’S THEORY OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

Zhang Yi¹, Mei Fengxiang²

1. Suzhou Institute of Urban Construction & Environmental Protection, Suzhou 215011, P R China;
2. Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, P R China

Received:1997-12-08 Revised:1999-06-11 Online:2000-01-18 Published:2000-01-18
Supported by:
the National Natural Science Foundation of China(19572018);the Doctoral Programme Foundation of Institution of Higher Education of China

摘要/Abstract

摘要： Noether’s theory of dynamical systems with unilateral constraints by introducing the generalized quasi_symmetry of the infinitesimal transformation for the transformation group G_r is presented and two examples to illustrate the application of the result are given.

关键词: analytical mechanics, unilateral constraint, conservation law, symmetry, Noether’s theorem

Abstract: Noether’s theory of dynamical systems with unilateral constraints by introducing the generalized quasi_symmetry of the infinitesimal transformation for the transformation group G_r is presented and two examples to illustrate the application of the result are given.

Key words: analytical mechanics, unilateral constraint, conservation law, symmetry, Noether’s theorem

中图分类号:

O316

张毅;梅凤翔. NOETHER’S THEORY OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(1): 59-66.

Zhang Yi;Mei Fengxiang. NOETHER’S THEORY OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(1): 59-66.

[1]	Fan TANG, Weitao BI, Zhensu SHE. Multi-layer analytic solution for k-ω model equations via a symmetry approach[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(2): 289-306.
[2]	Shujuan AN, Kai TIAN, Zhaodong DING, Yongjun JIAN. Electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids in a microchannel[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 917-930.
[3]	Jingjing HU, Mengbo XU, Weipeng HU, Ruisong JIANG, Zichen DENG. Dynamic symmetry breaking and structure-preserving analysis on the longitudinal wave in an elastic rod with a variable cross-section[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(1): 81-92.
[4]	Lingyan TANG, Songhe SONG, Hong ZHANG. High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 173-192.
[5]	Lihua LIU, Chaolu TEMUER. Symmetry analysis of modified 2D Burgers vortex equation for unsteady case[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 453-468.
[6]	Zhijun SHEN, Xiao LI, Jian REN. Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(11): 1571-1586.
[7]	Yue WANG, Jiequan LI. Entropy convergence of new two-value scheme with slope relaxation for conservation laws[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(11): 1551-1570.
[8]	Yinshan YUN;Chaolu TEMUER. Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 365-378.
[9]	高芳;张晓波;傅景礼. Application of canonical coordinates for solving single-freedom constraint mechanical systems [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(8): 1029-1038.
[10]	吴春秀张鹏 S. C. WONG 乔殿梁戴世强. Solitary wave solution to Aw-Rascle viscous model of traffic flow[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(4): 523-528.
[11]	A. B. ROSMILA;R. KANDASAMY;I. MUHAIMIN. Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 593-604.
[12]	P. RAM;V. KUMAR. Effect of temperature dependent viscosity on revolving axi-symmetric ferrofluid flow with heat transfer[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(11): 1441-1452.
[13]	M. NADJAFIKHAH R. BAKHSHANDEH CHAMAZKOTI F. AHANGARI. Potential symmetries and conservation laws for generalized quasilinear hyperbolic equations[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(12): 1607-1614.
[14]	J.KONG D.THUNG. Convergence and exact solutions of spline finite strip method using unitary transformation approach[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(11): 1407-1422.
[15]	李昭祥杨忠华. Bifurcation method for solving multiple positive solutions to boundary value problem of p-Henon equation on the unit disk[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(4): 511-520.

NOETHER’S THEORY OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

NOETHER’S THEORY OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价