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The Lie symmetries and noether conserved quantities of discrete mechanical systems with variable mass

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Chinese Physics B 2008年第3期17卷 754-758页

作者：施沈阳傅景礼黄晓虹陈立群张晓波 Department of Physics Zhejiang Sci-Tech University Shanghai Institute of Applied Mathematics and Mechanics Shanghai University School of Physics and Electronic Information Wenzhou University

This paper studies the Lie symmetries and noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.

关键词： discrete mechanics variable mass system Lie symmetry noether conserved quantity

noether-Lie Symmetry of Generalized Classical Mechanical Systems

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Communications in Theoretical Physics 2008年第2期49卷 305-307页

作者： ZHANG Xiao-Ni FANG Jian-Hui WANG Peng DING Ning College of Physics Science and Technology China University of Petroleum Dongying 257061. China

In this paper, the noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The noether conserved quantity and the Hojman conserved quantity deduced from the noether Lie symmetry are obtained. An example is given to illustrate the application of the results.

关键词： generalized classical mechanical system noether-Lie symmetry noether conserved quantity Hojman conserved quantity

Lie symmetries and conserved quantities for generalized Birkhoff system

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Journal of Beijing Institute of Technology 2011年第3期20卷 285-288页

作者：梅凤翔崔金超 School of Aerospace Engineering Beijing Institute of Technology

To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A con- served quantity of Hojman＇ s type and a noether＇ s conserved quantity are deduced by the Lie symme- try under some conditions. One example is given to illustrate the application of the result.

关键词： generalized Birkhoff system Lie symmetry noether conserved quantity conservedquantity of Hojman' s type

A structure-preserving algorithm for time-scale non-shiftedHamiltonian systems

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Theoretical & Applied Mechanics Letters 2022年第5期12卷 349-358页

作者： Xue Tian Yi Zhang School of Science Nanjing University of Science and TechnologyNanjing210094JiangsuChina School of Mathematics and Big Data Anhui University of Science and TechnologyHuainan232001AnhuiChina College of Civil Engineering Suzhou University of Science and TechnologySuzhou215011JiangsuChina

The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational *** only can the combination ofand∇derivatives be beneficial to obtaining higher convergence order in numerical analysis,but also it prompts the timescale numerical computational scheme to have good properties,for instance,*** this letter,a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is *** using the time-scale discrete variational method and calculus theory,and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems,the corresponding discrete Hamiltonian principle can be ***,the time-scale discrete Hamilton difference equations,noether theorem,and the symplectic scheme of discrete Hamiltonian systems are ***,taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples,they show that the time-scale discrete variational method is a structure-preserving *** new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed.

关键词： Time-scale non-shifted system Hamiltonian system Structure-preserving algorithm noether conserved quantity