Conformal invariance for nonholonomic system of Chetaev’s type with variable mass

Conformal invariance and conserved quantities for a nonholonomic system of Chetaev’s type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system’s conformal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.     

力和电场强度叠加原理的相对论分析

本文用狭义相对论分别分析了力和电场强度的叠加原理。     

用四元数证明欧拉位移定理

采用四元数方法对欧拉位移定理进行证明。     

Lagrange系统Lie点变换下的共形不变性与守恒量

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. 关键词： Lagrange系统 Lie点变换 共形不变性 守恒量     

液晶

液晶是１８８８年奥地利植物学家莱尼茨尔在合成胆醇脂时发现的：实验物质加热到１４５℃晶体开始熔解并逐渐变成乳白色粘稠状液体,温度达到１７８．５℃时粘稠状液体变清而成为各向同性的液体．该物质处于１４５－１７８．５℃之间的粘稠状态时具有双折射现象,这就是液晶．２０世纪６０年代以后液晶研究篷勃发展起来．７０年代法国物理学家德然纳成功地建立了液晶的宏观相变理论并提出了液晶与超导体和超流体的相似性,使液晶成为一门独立的学科．德然纳因此项成就获得１９９１年诺贝尔物理奖．我国从７０年代开始液晶的研究和开发工作,…     

工科物理概念结构体系现代化

 根据原国家教委布置,当前我国工程教育改革的基本思路是加强基础、淡化专业、提高素质、培养宽口径科技人才,以便同国际工程教育接轨。国家教委在“面向２１世纪工程教育教学内容课程体系改革计划”中确定了４项目标：①要使学生的素质和知识结构适应２１世纪我国社会主义建设的需要;②要使教学内容和课程体系达到或接近世界先进水平;③要使教学手段、教学方法现代化;④要使学生的创新能力和工程实践能力有比较大的加强。总而言之,就是我国的工程教育要现代化。工程教育的现代化要以物理教育的现代化为基础。我国传统的工科物理内容结构体系与此不相适应,必须尽快进行改革,改革的重点是实现概念结构体系的现代化。     

Chetaev型非完整系统Mei对称性的共形不变性与守恒量

研究Chetaev型非完整系统Mei对称性的共形不变性与守恒量.引入无限小单参数变换群及其生成元向量,给出与Chetaev型非完整系统相应的完整系统的Mei对称性共形不变性定义和确定方程.讨论系统共形不变性与Mei对称性的关系.利用限制方程和附加限制方程得到非完整系统弱Mei对称性和强Mei对称性的共形不变性.借助规范函数满足的结构方程导出系统相应的守恒量,并举例说明结果的应用.     

有心力运动轨道的切线坐标解法

采用切线坐标讨论了质点在有心力场中的运动轨道，导出了动力参数和几何参数形式的切线坐标方程以及极坐标方程。     

A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

For the relativistic holonomic nonconservative system, a new Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the theory of invariance of differential equations of motion under infinitesimal transformations for t and qs, we construct the relativistic Lie symmetrical determining equations and obtain directly a new relativistic Lie symmetrical non-Noether conserved quantity of the system, which only depend on the variables t, qs and qs. An example is given to illustrate the application of the results.     

Conformal invariance and conserved quantity of Hamilton systems

This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.