完整系统Nielsen方程的统一对称性与守恒量

研究完整系统Nielsen方程的统一对称性与守恒量.在完整系统Nielsen方程的基础上,首先给出了Nielsen方程的Noether对称性、Lie对称性和Mei对称性与守恒量,其次给出了Nielsen方程的统一对称性的定义和判据,得到Nielsen方程的统一对称性导致的Noether守恒量、Hojman守恒量和Mei守恒量.举例说明结果的应用.     

Two New Types of Conserved Quantities Deduced from Noether Symmetry for Nonholonomic Mechanical System

For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.     

Kepler方程的Noether对称性与Hojman守恒量

研究Kepler方程的Noether对称性与Hojman守恒量.给出系统的运动微分方程并给出Noether对称性的确定方程,提出Kepler方程的Noether对称性导致的Hojman守恒量.     

Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量

研究Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量. 对Chetaev型约束的相对运动力学系统Nielsen方程的运动微分方程、Noether对称性定义和判据进行具 体的研究, 得到了Noether对称性直接导致的Noether守恒量的表达式. 最后举例说明结果的应用.     

Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量

研究Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量. 对Chetaev型约束的相对运动力学系统Nielsen方程的运动微分方程、Noether对称性定义和判据进行具 体的研究, 得到了Noether对称性直接导致的Noether守恒量的表达式. 最后举例说明结果的应用.     

Rosenberg问题的Noether-Lie对称性与守恒量

研究Rosenberg问题的对称性与守恒量.给出Rosenberg问题的Noether-Lie对称性的定义和判据,以及由Noether-Lie对称性导出Noether守恒量和Hojman守恒量. 关键词： 非完整系统 Noether-Lie对称性 守恒量     

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

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.     

非保守力与非完整约束对Lagrange系统Noether对称性的影响

研究非保守力和非完整约束对Lagrange系统的Noether对称性的影响. Lagrange系统受到非保守力或非完整约束作用时，系统的Noether对称性和守恒量都会发生变化. 原有的一些Noether对称性消失了，一些新的Noether对称性产生了，在一定条件下，一些Noether对称性仍保持不变. 分别给出系统的Noether对称性以及守恒量保持不变的条件，并举例说明结果的应用. 关键词： Lagrange系统 非保守力 非完整约束 Noether对称性     

广义非完整力学系统的Lie对称性与Noether守恒量

研究广义非完整力学系统的Lie对称性与Noether守恒量,建立Lie对称性的确定方程、限制方程和附加限制方程,给出结构方程和Noether守恒量的形式,研究Lie对称性的逆问题,并举算例说明结果的应用.     

均匀磁场中二维各向同性带电谐振子的守恒量与对称性研究

由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程.     

相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用. 关键词： 相空间 离散完整系统 对称性 守恒量     

The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems

This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results.     

Conformal Invariance and Noether Symmetry,Lie Symmetry of Birkhoffian Systems in Event Space

This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

阻尼谐振子的拉格朗日函数和哈密顿函数

利用一种直接方法将阻尼谐振动微分方程变换成等价的自伴随形式,并构造出阻尼振子的两个拉格朗日函数和哈密顿函数,导出了阻尼谐振子的Noether守恒量.     

Noether Symmetry Can Lead to Non-Noether Conserved Quantity of Holonomic Nonconservative Systems in General Lie Transformations

For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first, the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of non-Noether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.     

离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量

本文研究离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量. 构建了离散差分序列变质量Hamilton系统的差分动力学方程, 给出了离散差分序列变质量Hamilton系统差分动力学方程在无限小变 换群下的Lie对称性的确定方程和定义, 得到了离散力学系统Lie对称性导致Noether守恒量的条件及形式, 举例说明结果的应用. 关键词： 离散力学 Hamilton系统 Lie对称性 Noether守恒量     

Noether Symmetry and Noether Conserved Quantity of Nielsen Equation for Dynamical Systems of Relative Motion

Noether symmetry of Nielsen equation and Noether conserved quantitydeduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.     

约束对Birkhoff系统Noether对称性和守恒量的影响

研究约束对Birkhoff系统的Noether对称性和守恒量的影响．首先，建立了Birkhoff系统的运动微分方程．其次，给出了系统Noether对称性的判据．然后，讨论了受约束作用后，Birkhoff系统的Noether对称性发生的变化，并给出了系统的Noether对称性以及守恒量保持不变的条件．最后，举例说明结果的应用． 关键词： 分析力学 Birkhoff系统 约束 Noether对称性 守恒量     

含时滞的非保守系统动力学的Noether对称性

提出并研究含时滞的非保守系统动力学的Noether对称性与守恒量. 首先,建立含时滞的非保守系统的Hamilton原理,得到含时滞的Lagrange方程;其次,基于含时滞的Hamilton作用量在依赖于广义速度的无限小群变换下的不变性,定义系统的Noether对称变换和准对称变换,建立Noether对称性的判据;最后,研究对称性与守恒量之间的关系,建立含时滞的非保守系统的Noether理论. 文末举例说明结果的应用. 关键词： 时滞系统 非保守力学 Noether对称性 守恒量     

Exact solutions and conserved quantities in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper explores Noether and Noether gauge symmetries of anisotropic universe model in f(R, T) gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.