FIRST INTEGRALS AND INTEGRAL INVARIANTS FOR VARIABLE MASS NONHOLONOMIC SYSTEM IN NONINERTIAL REFERENCE FRAMES

ＦＩＲＳＴＩＮＴＥＧＲＡＬＳＡＮＤＩＮＴＥＧＲＡＬＩＮＶＡＲＩＡＮＴＳＦＯＲＶＡＲＩＡＢＬＥＭＡＳＳＮＯＮＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭＩＮＮＯＮＩＮＥＲＴＩＡＬＲＥＦＥＲＥＮＣＥＦＲＡＭＥＳＬｕｏＳｈａｏ－ｋａｉ（罗绍凯）（Ｓｈａｎｇｑｉｕ，Ｎｏｒ...     

INTEGRATION METHOD FOR THE DYNAMICS EQUATION OF RELATIVE MOTION OF VARIABLE MASS NONLINEAR NONHOLONOMIC SYSTEM

1.IntroductionMoreandmoreattentionhasbeenpaidtothestudyofdynamicsofcomplicatedsystemwiththedevelopmentofmodernscienceandtechnology.Thestudyoftherelativemotionofvariablemasssystembyusingthetheoryandmethodofanalyticalmechanicsnotonlycanunifytheexpressionformbutalsocandisplayitssuperioritytothecomplicatedsystem.In1961,thedynamicsofrelativemotionofholonomicsystemwasderivedbyLur'ell].Inrecehtyears,LiulZIandLuol3'4]havegiventhedynamicsequationsofrelativemotionofvariablemassnonholonomicsystem.Howe…     

相对运动动力学系统Appell方程Mei对称性导致的Mei守恒量

研究相对运动动力学系统Appell方程的Mei对称性及其直接导致的Mei守恒量.在群的无限小变换下,给出相对运动动力学系统Appell方程Mei对称性的定义和判据;得到相对运动动力学系统Appell方程Mei对称性的结构方程以及Mei对称性直接导致的Mei守恒量的表达式.举例说明结果的应用. 关键词： 相对运动动力学 Appell方程 Mei对称性 Mei守恒量     

奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性

研究奇异系统Hamilton正则方程的形式不变性即Mei对称性，给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明结果的应用. 关键词： 奇异系统 Hamilton正则方程 约束 对称性 守恒量     

A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and qs, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, qs and qs. A series of deductions are inferred for a holonomic nonconservative system,Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.     

Cyclic integrals and reduction of rotational relativistic Birkhoffian system

The order reduction method of the rotational relativistic Birkhoffian is studied.For a rotational relativistic Birkhoffian system.the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the rotational relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the results.     

变质量非完整系统相对于非惯性系的第一积分与积分不变量

本文给出了变质量非完整系统相对于非惯性系的第一积分存在的条件，建立了这类系统的正则方程和变分方程，证明了由第一积分可直接构造系统的积分不变量，并给出一系列推论和一个例子．     

约束Birkhoff系统的形式不变性

约束Birkhoff系统的形式不变性是约束Birkhoff方程的无限小变换下的一种不变性。给出约束Birkhoff系统形式不变性的定义与判据，并研究了这种形式不变性与Noether对称性之间的关系。     

从培养能力的角度看设计性实验

针对传统实验那种安排过死、刻板机械的特点，把设计性实验运用于教具设计与制作课程之中，充分地培养了学生动手、动脑的综合能力。     

转动系统的相对论性分析力学理论

本文讨论了转动相对论力学理论，主要是建立转动系统的相对论性分析力学理论·构造转动系统的相对论性广义动能函数Ｔｒ＝∑ｎｉ＝１Ｉ０ｉΓｉ２（１－１－θ·２ｉ／Γｉ２）和广义加速度能量函数Ｓｒ＝１２∑ｎｉ＝１Ｉｉ（θ·ｉ·θ¨ｉ）２Γｉ２－θ·２ｉ＋θ¨２ｉ，给出其Ｈａｍｉｌｔｏｎ原理和三种不同形式的Ｄ′Ａｌｅｍｂｅｒｔ原理；对于完整约束系统，建立了转动系统的相对论性Ｌａｇｒａｎｇｅ方程、Ｎｉｅｌｓｅｎ方程、Ａｐｐｅｌ方程和Ｈａｍｉｌｔｏｎ正则方程；对于非完整约束系统，建立了转动系统的相对论性Ｒｏｕｔｈ方程、Чаплыгин方程、Ｎｉｅｌｓｅｎ方程和Ａｐｐｅｌ方程；并给出转动系统的相对论性Ｎｏｅｔｈｅｒ守恒律