非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量

研究非保守系统广义Raitzin正则方程的形式不变性与非Noether守恒量.列出系统的Raitzin正则方程.提出在无限小变换下系统形式不变性的定义和判据.给出系统的形式不变性是Lie对称性的充要条件.建立Hojman守恒定理，并举例说明结果的应用. 关键词： 非保守系统 Raitzin正则方程 形式不变性 非Noether守恒量     

非完整系统Hamilton正则方程的形式不变性

研究非完整系统Hamilton正则方程的形式不变性，给出形式不变性的定义和判据，建立形式不变性和系统守恒量之间的关系，并举例说明结果的应用. 关键词： 非完整系统 Hamilton正则方程 形式不变性 守恒量     

广义Raitzin正则方程的Hojman守恒定理

利用时间不变的无限小变换下的Lie对称性，研究广义经典力学中Raitzin正则方程的Hojman 守恒定理。建立广义Raitzin正则方程。给出无限小变换下Lie对称性的确定方程。建立系统的Hojman守恒定理，并举例说明结果的应用。     

非线性非完整系统Raitzin正则方程的Hojman守恒定理

利用时间不变的无限小变换下的Lie对称性，研究非线性非完整系统Raitzin正则方程的Hojman守恒定理.列出系统的运动微分方程.建立时间不变的无限小变换下的确定方程.给出系统的Hojman守恒定理，并举例说明结果的应用. 关键词： 非线性非完整系统 Raitzin正则方程 Lie对称性 确定方程 Hojman守恒 定理     

完整非保守系统Raitzin正则运动方程的积分因子和守恒定理

提出了经典非保守动力学系统守恒定律构成的一般途径.首先,给出积分因子的定义.其次,详细地研究了守恒量存在的必要条件,建立了完整非保守系统Raitzin正则运动方程的守恒定理及其逆定理,并举例说明结果的应用 关键词： 完整系统 Raitzin正则方程 积分因子 守恒定律     

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     

广义经典力学中Hamilton-Tabarrok-Leech正则方程的对称性理论

提出广义Hamilton-Tabarrok-Leech正则方程的对称性理论.列写系统的运动方程.研究系统的Noether对称性、形式不变性和Lie对称性，并求出相应的守恒量.举例说明结果的应用. 关键词： 广义经典力学 H-T-L 正则方程 对称性 守恒量     

相空间中非完整非保守系统的形式不变性

研究相空间中非完整非保守系统的形式不变性.给出相空间中非完整非保守系统形式不变性的定义和判据，得到形式不变性的结构方程和守恒量形式，并举例说明结果的应用. 关键词： 相空间 非完整非保守系统 形式不变性     

相空间中二阶线性非完整系统的形式不变性

研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整系统形式不变性的定义和判据，得到形式不变性的结构方程和守恒量的形式，并举例说明结果的应用. 关键词： 相空间 二阶线性非完整系统 形式不变性 守恒量     

哈密顿Ermakov系统的形式不变性

把形式不变性的方法用于研究哈密顿Ermakov系统，从哈密顿Ermakov系统的形式不变性出发，运用比较系数法得到与形式不变性相应的点对称变换生成元的表达式及势能所满足的偏微分方程.结果表明，在点对称变换下，只有自治的哈密顿Ermakov系统才具有形式不变性. 关键词： 哈密顿Ermakov系统 拉格朗日函数 点对称变换 形式不变性     

Form Invariance of Raitzin's Canonical Equations of Relativistic Mechanical System

A form invariance of Raitzin's canonical equations of relativistic mechanical system is studied. First, the Raitzin's canonical equations of the system are established. Next, the definition and criterion of the form invariance in the system under infinitesimal transformations of groups are given. Finally, the relation between the form invariance and the conserved quantity of the system is obtained and an example is given to illustrate the application of the result.     

Lie symmetries and invariants of constrained Hamiltonian systems

According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.     

Form invariance for systems of generalized classical mechanics

This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. Ac-cording to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and estab-lishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is giver to illustrate the application of the results.     

Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system

A weakly nonholonomic system is a nonholonomic system whose constraint equations contain a small parameter. The form invariance and the approximate conserved quantity of the Appell equations for a weakly nonholonomic system are studied. The Appell equations for the weakly nonholonomic system are established, and the definition and the criterion of form invariance of the system are given. The structural equation of form invariance for the weakly nonholonomic system and the approximate conserved quantity deduced from the form invariance of the system are obtained. Finally, an example is given to illustrate the application of the results.     

Canonical symmetry of a constrained Hamiltonian system and canonical ward identity

An algorithm for the construction of the generators of the gauge transformation of a constrained Hamiltonian system is given. The relationships among the coefficients connecting the first constraints in the generator are made clear. Starting from the phase space generating function of the Green function, the Ward identity in canonical formalism is deduced. We point out that the quantum equations of motion in canonical form for a system with singular Lagrangian differ from the classical ones whether Dirac's conjecture holds true or not. Applications of the present formulation to the Abelian and non-Abelian gauge theories are given. The expressions for PCAC and generalized PCAC of the AVV vertex are derived exactly from another point of view. A new form of the Ward identity for gauge-ghost proper vertices is obtained which differs from the usual Ward-Takahashi identity arising from the BRS invariance.     

Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.