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1.
In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result. 相似文献
2.
研究非保守Nielsen方程由形式不变性直接导致的非Noether守恒量.函数对时间的全导数采 用沿运动轨道曲线的方式,给出非保守Nielsen方程的非点的形式不变性的定义和判据,并 研究其Noether守恒量.得到形式不变性导致非Noether守恒量的条件以及守恒量的形式,并 给出三种特殊情形的推论.举例说明结果的应用.
关键词:
Nielsen方程
形式不变性
非Noether守恒量 相似文献
3.
Using form invariance under special infinitesimal transformations
in which time is not variable, the non-Noether conserved quantity
of the relativistic nonholonomic system with variable mass is studied.
The differential equations of motion of the system are established.
The definition and criterion of the form invariance of
the system under infinitesimal transformations are studied.
The necessary and sufficient condition under which the form
invariance is a Lie symmetry is given. The condition under
which the form invariance can be led to a non-Noether conserved
quantity and the form of the conserved quantity are obtained.
Finally, an example is given to illustrate the application of the result. 相似文献
4.
研究Lagrange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.
关键词:
Lagrange系统
Mei对称性
守恒量 相似文献
5.
This paper studies a new conserved quantity which can be called
generalized Mei conserved quantity and directly deduced by Mei
symmetry of Birkhoff system. The conditions under which the Mei
symmetry can directly lead to generalized Mei conserved quantity and
the form of generalized Mei conserved quantity are given. An example
is given to illustrate the application of the results. 相似文献
6.
在时间不变的特殊无限小变换下,研究相对论性变质量非完整可控力学系统的非Noether守恒量——Hojamn守恒量.建立了系统的运动微分方程, 给出了系统在特殊无限小变换下的形式不变性(Mei对称性)的定义和判据以及系统的形式不变性是Lie对称性的充分必要条件.得到了系统形式不变性导致非Noether守恒量的条件和具体形式.举例说明结果的应用.
关键词:
相对论
非完整可控力学系统
变质量
非Noether守恒量 相似文献
7.
A form invariance and a conserved quantity of the generalised Birkhoffian system are studied.
Firstly, a definition and a criterion of the form invariance are given. Secondly, through the form invariance,
a new conserved quantity can be deduced. Finally,
an example is given to illustrate the application of the result. 相似文献
8.
A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical
system, is presented. Under general infinitesimal transformations, the
determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable
mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the
corresponding holonomic mechanical system, the weak Hojman conserved
quantity and the strong Hojman conserved quantity of the nonholonomic controllable mechanical system are obtained. An example is given to illustrate the application of the results. 相似文献
9.
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
10.
This paper focuses on studying non-Noether conserved quantities of Lie
symmetry and of form invariance for a mechanical system in phase space
under the general infinitesimal transformation of groups. We obtain a new
non-Noether conserved quantity of Lie symmetry of the system, and Hojman and
Mei's results are of special cases of our conclusion. We find a
condition under which the form invariance of the system will lead to a Lie
symmetry, and, further, obtain a new non-Noether conserved quantity of form
invariance of the system. An example is given finally to illustrate these
results. 相似文献
11.
Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system
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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. 相似文献
12.
13.
This paper focuses on studying the relation between a velocity-dependent symmetry and a generalized Lutzky conserved quantity for a holonomic system with remainder coordinates subjected to unilateral constraints. The differential equations of motion of the system are established, and the definition of Lie symmetry for the system is given.The conditions under which a Lie symmetry can directly lead up to a generalized Lutzky conserved quantity and the form of the new conserved quantity are obtained, and an example is given to illustrate the application of the results. 相似文献
14.
This paper focuses on studying a Hojman conserved quantity directly
derived from a Lie symmetry for a Birkhoffian system in the event space.
The Birkhoffian parametric equations for the system are established, and
the determining equations of Lie symmetry for the system are obtained.
The conditions under which a Lie symmetry of Birkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojman conserved quantity are given. An example is given to illustrate
the application of the results. 相似文献
15.
This paper studies the Lie symmetry and Hojman conserved quantity of the Nambu system. The determining equations of Lie symmetry for the system are given. The conditions for existence and the form of the Hojman conserved quantity led by the Lie symmetry for the system are obtained. Finally, an example is given to illustrate the application of the results. 相似文献
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18.
研究一类非完整系统运动方程的Lie对称性与Hojman型守恒量.给出系统Lie对称性的确定方程和限制方程,存在守恒量的条件以及守恒量的形式.举例说明结果的应用.
关键词:
分析力学
非完整系统
对称性
Hojman型守恒量 相似文献
19.
ZHANG Xiao-Ni FANG Jian-Hui LIN Peng PANG Ting 《理论物理通讯》2008,49(5):1145-1147
In this paper, a new type of conserved quantity directly deduced from the Mei symmetry for relativistic variable mass system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results. 相似文献