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Lagrange系统Lie点变换下的共形不变性与守恒量
  • ISSN号：1000-3290
  • 期刊名称：《物理学报》
  • 时间：0
  • 分类：O316[理学—一般力学与力学基础;理学—力学] O174.51[理学—数学;理学—基础数学]
  • 作者机构：[1]杭州师范大学理学院,杭州310018, [2]北京理工大学理学院,北京100081
  • 相关基金：国家自然科学基金（批准号：10572021,10772025）和高等学校博士学科点专项科研基金（批准号：20040007022）资助的课题.
作者： 蔡建乐[1,2], 梅凤翔[2]
关键词： Lagrange系统, Lie点变换, 共形不变性, 守恒量, Lagrange system, Lie point transformation, conformal invariance, conserved quantity
中文摘要：

研究Lagrange系统Lie点变换下的共形不变性与守恒量,给出Lagrange系统的共形不变性定义和确定方程,讨论系统共形不变性与Lie对称性的关系,得到在无限小单参数点变换群作用下系统共形不变性同时是Lie对称性的充要条件,导出系统相应的守恒量,并给出应用算例.

英文摘要：

Conformal invariance and conserved quantities of Lagrange system under Lie point transformation are studied. Firstly, the definition of conformal invariance and determining equation for the Lagrange system are provided. Secondly, the relationship between the system＇s eonformal invariance and Lie symmetry are discussed; the necessary and sufficient condition on which the system＇ s conformal invarianee would be Lie symmetry under the infinitesimal one-parameter point transformation group is deduced; and the eonserved quantities of the system are given. Lastly, an illustration example is introduced.

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Weakly Noether symmetry for nonholonomic systems of non-Chetaev type
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一类广义Birkhoff系统的广义正则变换
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广义Birkhoff方程的积分方法
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广义Birkhoff系统的一类积分
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一般完整系统Mei对称性的共形不变性与守恒量
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理论力学可视化教学与Matlab/Simulink
Conformal invariance and conserved quantity of Hamilton systems
Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations
Symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type
A potential integration method for Birkhoffian system
Poisson theory of generalized Bikhoff equations
Conformal invariance and Hojman conserved quantities of first order Lagrange systems
Lie symmetries and generalized conserved quantities for Birkhoff system
Weak Noether symmetry and conserved laws of Birkhoffian systems
Form invariance and new conserved quantity of generalised Birkhoffian system
Stability for manifolds of equilibrium states of generalized Birkhoff system
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Symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates
相对运动动力学系统的Lagrange对称性
广义Birkhoff系统动力学的一类逆问题
广义Birkhoff系统的积分不变量
Weak Noether symmetry and non-Noether conserved quantities for general holonomic systems
Analytical mechanics methods for solving Whittaker equations
Lagrange 系统的弱Noether对称性
Weakly Noether symmetry for nonholonomic systems of Chetaev’s type
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三质点Toda晶格微分方程的积分
广义Birkhoff系统动力学的基本框架
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微分方程借助辅助变量的Hamilton化与求解
Symmetry of Lagrangians of nonholonomic systems
Nondassical potential symmetries and invariant solutions of heat equation
A Birkhoff-Noether method of solving differential equations
On the Rosen-Edelstein model and the theoretical foundation of nonholonomic mechanics
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Hojman conserved quantity deduced be weak Noether symmetry for Lagrange systems
A conformal invariance for generalized Birkhoff equations
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A symmetry and a conserved quantity for the Birkhoff system
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求解微分方程的Hojman方法
Stability with respect to partial variables for Birkhoff systems
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广义Hamilton系统的共形不变性与Hojman守恒量
关于Noether对称性的两种理解
Potential method of integration for solving the equations of mechanical systems
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弱非完整系统的近似守恒量
一般完整系统Mei对称性的共形不变性与守恒量
Conformal invariance and conserved quantity of Hamilton systems
Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations
A potential integration method for Birkhoffian system
Poisson theory of generalized Bikhoff equations
Conformal invariance and Hojman conserved quantities of first order Lagrange systems
Stability with respect to partial variables for Birkhoff systems
Lagrange系统的弱Noether对称性
Lagrange系统Mei对称性的Ⅲ型结构方程和Ⅲ型Mei守恒量
相对运动动力学系统Nielsen方程的Lie对称性与Hojman守恒量
事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性与Mei守恒量
广义Birkhoff系统的时间积分定理
Chetaev型约束力学系统Appell方程的Lie对称性与守恒量
变质量完整动力学系统的共形不变性与守恒量
Appell方程Mei对称性导致的一种新型守恒量
事件空间中Birkhoff系统的Noether理论
事件空间中Birkhoff系统的参数方程及其第一积分
非完整系统Nielsen方程的Mei对称性与Mei守恒量
一类完整系统的Mei对称性与守恒量
一类非完整系统运动微分方程的Lie对称性与Hojman型守恒量
Maggi方程的形式不变性与Hojman守恒量
事件空间中单面非Chetaev型非完整约束系统的Mei守恒量
事件空间中非Chetaev型非完整系统的Mei对称性与Mei守恒量
事件空间中非Chetaev型非完整约束系统的Hojman守恒量
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Lie Symmetry and Hojman Conserved Quantity of Maggi Equations
Birkhoff系统的局部能量积分
Lagrange系统的特殊Noether-Lie对称性和特殊守恒量
完整系统Appell方程Mei对称性的结构方程和Mei守恒量
Chetaev型约束力学系统Appell方程的Mei对称性与Mei守恒量
Pfaff约束可积的Euler形式的充分条件
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A type of new conserved quantity deduced from Mei symmetry for Appell equations in a holonomic system with unilateral constraints
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Stability of Controlled Hamilton Systems Excited by Gaussian White Noise
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Constraint Stabilization and One-Step Correction Method for Dynamical Systems
Conformal invariance and Hojman conserved quantities of canonical Hamilton systems
Conformal Invariance and Noether Conserved Quantities of First-Order Lagrange Systems
Field Method for Integrating the First Order Differential Equation
Mei Symmetry and Mei Conserved Quantity for a Non-holonomic System of Non-Chetaev＇s Type with Unilateral Constraints in Nielsen Style
Mei conserved quantity of the Nielsen equation for a non-Chetaev-type non-holonomic system
First integrals and stability of second-order differential equations
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Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system
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Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints
Lagrange-Noether method for solving second-order differential equations
On the Rosen-Edelstein model and the theoretical foundation of nonholonomic mechanics
一般完整系统Appell方程的Mei对称性
Noether＇s theorem and one-step corrections method for holonomic system
Conserved quantities and symmetries related to stochastic Hamiltonian systems
期刊信息
  • 《物理学报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国物理学会 中国科学院物理研究所
  • 主编：欧阳钟灿
  • 地址：北京603信箱(中国科学院物理研究所)
  • 邮编：100190
  • 邮箱：apsoffice@iphy.ac.cn
  • 电话：010-82649026
  • 国际标准刊号：ISSN：1000-3290
  • 国内统一刊号：ISSN：11-1958/O4
  • 邮发代号:2-425
  • 获奖情况:
  • 1999年首届国家期刊奖,2000年中科院优秀期刊特等奖,2001年科技期刊最高方阵队双高期刊居中国期刊第12位
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  • 被引量:49876