一类新型正则方程对广义经典力学的推广

本文首先将一类新型正则方程推广到广义经典力学,得到广义正则方程,确定泊松括号和拉格朗日括号及它们的性质,用泊松括号表示广义正则方程,建立新型Hamilton广义变分原理、Hamilton-jacobi方程。     

NOETHER’S CONSERVATION LAWS OF HOLONOMIC NONCONSERVATIVE DYNAMICAL SYSTEMS IN GENERALIZED MECHANICS

ＮＯＥＴＨＥＲ’ＳＣＯＮＳＥＲＶＡＴＩＯＮＬＡＷＳＯＦＨＯＬＯＮＯＭＩＣＮＯＮＣＯＮＳＥＲＶＡＴＩＶＥＤＹＮＡＭＩＣＡＬＳＹＳＴＥＭＳＩＮＧＥＮＥＲＡＬＩＺＥＤＭＥＣＨＡＮＩＣＳＱｉａｏＹｏｎｇ－ｆｅｎ（乔永芬）ＹｕｅＱｉｎｇ－ｗｅｎ（岳庆文）（Ｎｏ...     

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     

准坐标下广义力学系统的Lie对称定理及其逆定理

研究准坐标下广义力学系统的Lie对称性与守恒量.首先,对准坐标下广义力学系统定义无限小生成元,并应用微分方程在无限小变换下不变性的Lie方法,建立系统的确定方程.其次,给出结构方程和守恒量的形式.最后,研究Lie对称性逆问题(由已知积分求Lie对称)并举例说明结果的应用. 关键词： 广义力学 准坐标 Lie对称 确定方程 结构方程 守恒量     

高维增广相空间中广义力学系统的对称性和不变量

依据广义增广相空间中的Hamilton作用量在无穷小变换群作用下的不变性,给出广义完整保守和非保守力学系统的对称性和不变量及有关结论的逆命题,最后举一实例说明 关键词： 增广相空间 广义力学 对称性 不变量     

非完整转动相对论系统的Lindel?f方程

由转动相对论系统的Hamilton原理分别建立在广义坐标和准坐标下的Lindel?f方程及其改进形式,并从改进的Lindel?f方程导出新Chaplygin方程.最后说明由转动系统的相对论分析力学向普通分析力学过渡的方法. 关键词： 非完整约束 转动系统 相对论 Lindel?f方程 Chaplygin方程     

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.     

Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the nonholonomic Vacco dynamical system with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the system under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally an example is given to illustrate the application of the result.