事件空间中非完整非保守系统的守恒量存在定理及其逆定理

提出了事件空间中非完整非保守系统守恒定律构成的一般途径.首先，列写系统的运动微分方程，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，并建立了事件空间中非完整非保守系统的守恒量存在定理及其逆定理.最后，举例说明结果的应用. 关键词： 事件空间 非完整非保守系统 积分因子 守恒定理     

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     

非完整力学系统Raitzin正则方程的形式不变性

研究非完整力学系统Raitzin正则方程的形式不变性。建立系统的Raitzin正则方程。给出在无限小变换下系统形式不变性的定义和判据。得到系统的守恒量与形式不变性之间的关系并举例说明结果的应用。     

用积分因子方法研究非完整约束系统的守恒律

用积分因子方法研究非线性非完整约束系统的守恒律.给出了非完整约束系统的Routh方程的积分因子的定义，研究了守恒量存在的必要条件，建立了系统的守恒定理及其逆定理，并举例说明结果的应用. 关键词： 非完整约束系统 积分因子 守恒律 Killing方程     

准坐标下广义非保守系统Lagrange方程的积分因子与守恒定理

用积分因子方法研究准坐标下广义非保守系统Lagrange方程的守恒定理.列写系统的运动微分方程，给出它的积分因子的定义.研究守恒量存在的必要条件.建立系统的守恒定理及其逆定理，并举例说明结果的应用. 关键词： 准坐标 Lagrange方程 积分因子 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     

广义经典力学与非完整力学的统一理论

建立广义经典力学与非完整力学的统一理论———广义非完整力学理论,构造其基本框架.提出广义非完整力学的Чeтаeв(Chetaev)定义,建立广义非完整力学系统的Routh方程和正则方程.给出广义非完整力学系统的非等时变分方程,证明由广义非完整力学系统的第一积分可以构造积分不变量.研究广义非完整力学系统作用量的非等时变分,给出系统的Poincar啨Cartan积分变量关系和积分不变量,进而给出等时变分下系统的Poincar啨积分变量关系和通用积分不变量.给出一些推论,表明广义经典力学和一阶至高阶非完整力学的相关结论均为广义非完整力学理论的特款. 关键词： 广义非完整力学 广义Чeтаeв定义 运动方程 积分不变量     

非Chetaev型非完整系统的Lagrange对称性与守恒量

研究非Chetaev型非完整非保守力学系统的Lagrange对称性.给出了系统的Lagrange对称性的定义和判据,得到了非Chetaev型非完整非保守力学系统的Lagrange对称性导致守恒量（第一积分)的条件及其形式.举例说明结果的应用. 关键词： 非Chetaev型非完整约束 Lagrange对称性 守恒量     

一类可用Hamilton-Jacobi方法求解的非保守Hamilton系统

Hamilton-Jacobi方法通常被认为是求解完整保守Hamilton系统正则方程的重要手段,但通过现代微分几何理论发现,这种方法的适用范围不仅仅局限于完整保守的Hamilton系统.根据Hamilton-Jacobi理论,证明了经典Hamilton-Jacobi方法可以被推广至一类特殊的非保守Hamilton系统,即如果非保守Hamilton系统受到非保守力,则该系统的Hamilton正则方程也可以用Hamilton-Jacobi方法求解;对于这类非保守Hamilton系统,只要能够找到其对应的Hamilton-Jacobi方程的一个完全解,就可以得到系统正则方程的全部第一积分.经典的Hamilton-Jacobi方法则是上述方法的一个特例.     

Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton‘s canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.     

Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results.     

Integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics

In this paper,we present a general approach to the construction of conservation laws for generalized classical dynamical systems.Firstly,we give the definition of integrating factors and ,secondly,we study in detail the necessary conditions for the existence of conserved quantities.Then we establish the conservation theorem and its inverse for the hamilton‘s canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics.Finally,we give an example to illustrate the application of the results.     

Poincare-Cartan Integral Invariants of Nonconservative Dynamical Systems

Traditionally there do not exist integralinvariants for a nonconservative system in the phasespace of the system. For weak nonconservative systems,whose dynamical equations admit adjoint symmetries, there exist Poincare and Poincare-Cartanintegral invariants on an extended phase space, wherethe set of dynamical equations and their adjointequations are canonical. Moreover, integral invariantsalso exist for pseudoconservative dynamical systemsin the original phase space if the adjoint symmetriessatisfy certain condtions.     

Variational principle and dynamical equations of discrete nonconservative holonomic systems

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler--Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.     

Noether symmetries of discrete mechanico-electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.     

约束哈密顿系统在相空间中的精确不变量与绝热不变量

研究小干扰力作用下约束哈密顿系统对称性的摄动问题.建立了非保守约束哈密顿系统的正则方程,在增广相空间中研究了系统的对称性与精确不变量.基于力学系统的高阶绝热不变量的概念,给出了系统的各阶绝热不变量的形式及存在条件,并建立了绝热不变量与对称变换之间的对应关系 关键词： 约束哈密顿系统 对称性 摄动 不变量