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This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result in the end. 相似文献
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The symmetry of Lagrangians of a holonomic variable mass system is studied.Firstly,the differential equations of motion of the system are established.Secondly,the definition and the criterion of the symmetry of the system are presented.Thirdly,the conditions under which there exists a conserved quantity deduced by the symmetry are obtained.The form of the conserved quantity is the same as that of the constant mass Lagrange system.Finally,an example is shown to illustrate the application of the result. 相似文献
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This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result at the end. 相似文献
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This paper studies the symmetry of Lagrangians of
nonholonomic systems of non-Chetaev's type. First, the definition
and the criterion of the symmetry of the system are given. Secondly,
it obtains the condition under which there exists a conserved
quantity and the form of the conserved quantity. Finally, an example
is shown to illustrate the application of the result. 相似文献
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A New type of conserved quantity deduced from Mei symmetry of nonholonomic systems in terms of quasi-coordinates 下载免费PDF全文
This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the
application of the nonholonomic system's results. 相似文献
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研究一般完整力学系统的Mei对称性直接导致的一种守恒量,给出系统的Mei对称性的定义和判据方程,得到系统Mei对称性直接导致的一种守恒量的条件和形式,并举例说明结果的应用. 相似文献
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研究一般完整系统Mei对称性的共邢不变性与守恒量.引入无限小单参数变换群及其生成元向量,定义一般完整系统动力学方程的Mei对称性共形不变性,借助Euler算子导出Mei对称性共形不变性的相关条件,给出其确定方程.讨论共形不变性与Noether对称性、Lie对称性以及Mei对称性之间的关系.利用规范函数满足的结构方程得到系统相应的守恒量.举例说明结果的应用.
关键词:
一般完整系统
Mei对称性
共形不变性
守恒量 相似文献
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A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations 总被引:1,自引:0,他引:1 下载免费PDF全文
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. 相似文献
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Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations 总被引:1,自引:0,他引:1 下载免费PDF全文
For a relativistic holonomic nonconservative system, by using the
Noether symmetry, a new non-Noether conserved quantity is given under
general infinitesimal transformations of groups. On the basis of the
theory of invariance of differential equations of motion under
general infinitesimal transformations, we construct the relativistic
Noether symmetry, Lie symmetry and the condition under which the
Noether symmetry is a Lie symmetry under general infinitesimal
transformations. By using the Noether symmetry, a new relativistic
non-Noether conserved quantity is given which only depends on the
variables $t$, $q_s $ and $\dot {q}_s $. An example is given to
illustrate the application of the results. 相似文献
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对一类完整系统的方程给出其Mei对称性的定义和判据.如果Mei对称性是Noether对称性,则可找到Noether守恒量.如果Mei对称性是Lie对称性,则可找到Hojman型守恒量.举例说明结果的应用.
关键词:
分析力学
完整系统
Mei对称性
守恒量 相似文献
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动力学逆问题是星际航行学、火箭动力学、规划运动学理论的基本问题. Mei对称性是力学系统的动力学函数在群的无限小变换下仍然满足系统原来的运动微分方程的一种新的不变性. 本文研究广义坐标下一般完整系统的Mei对称性以及与Mei对称性相关的动力学逆问题. 首先, 给出系统动力学正问题的提法和解法. 引入时间和广义坐标的无限小单参数变换群, 得到无限小生成元向量及其一次扩展. 讨论由n个广义坐标确定的一般完整力学系统的运动微分方程, 将其Lagrange函数和非势广义力作无限小变换, 给出系统运动微分方程的Mei对称性定义, 在忽略无限小变换的高阶小量的情况下得到Mei对称性的确定方程, 借助规范函数满足的结构方程导出系统Mei对称性导致的Noether守恒量. 其次, 研究系统Mei对称性的逆问题. Mei对称性的逆问题的提法是: 由已知守恒量来求相应的Mei对称性. 采取的方法是将已知积分当作由Mei对称性导致的Noether守恒量, 由Noether逆定理得到无限小变换的生成元, 再由确定方程来判断所得生成元是否为Mei对称性的. 然后, 讨论生成元变化对各种对称性的影响. 结果表明, 生成元变化对Noether和Lie对称性没有影响, 对Mei 对称性有影响, 但在调整规范函数时, 若满足一定条件, 生成元变化对Mei对称性也可以没有影响. 最后, 举例说明结果的应用. 相似文献