共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
5.
6.
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
7.
Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass 总被引:1,自引:0,他引:1 下载免费PDF全文
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. 相似文献
8.
For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and q_s, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, q_s and \dot{q}_s. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results. 相似文献
9.
FANGJian-Hui PENGYong LIAOYong-Pan LIHong 《理论物理通讯》2004,42(3):440-442
In this paper, we study the Lie symmetrical non-Noether conserved quantity of the differential equations of motion of mechanical system in phase space under the general infinitesimal transformations of groups. Firstly. we give the determining equations of the Lie symmetry of the system. Secondly, the non-Noether conserved quantity of the Lie symmetry is derived. Finally, an example is given to illustrate the application of the result. 相似文献
10.
For the holonomic nonconservative
system, by using the Noether symmetry, a non-Noether conserved quantity is
obtained directly under general infinitesimal transformations of groups in which time is variable. At first, the Noether symmetry, Lie symmetry, and
Noether conserved quantity are given. Secondly, the condition under which
the Noether symmetry is a Lie symmetry under general infinitesimal
transformations is obtained. Finally, a set of non-Noether conserved
quantities of the system are given by the Noether symmetry, and an example is
given to illustrate the application of the results. 相似文献
11.
研究相对论性转动变质量非完整可控力学系统的非Noether守恒量——Hojman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Mei对称性(形式不变性) 和Lie对称性的定义和判据, 以及系统的Mei对称性是Lie对称性的充分必要条件. 得到了系统Mei对称性导致非Noether守恒量的条件和具体形式. 举例说明结果的应用.
关键词:
相对论性转动
可控力学系统
变质量
非Noether守恒量 相似文献
12.
研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程;给出了系统的Lie对称性和Mei对称性的定义和判据;对于单面非Chetaev型非完整系统,证明了在一定条件下,由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量,由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量;研究了对称性和新守恒量之间的相互关系.文末,举例说明结果的应用.
关键词:
分析力学
单面约束
非完整系统
对称性
Hojman守恒量
Mei守恒量 相似文献
13.
The Lie symmetrical non-Noether conserved quantity of holonomic Hamiltonian system 总被引:1,自引:0,他引:1 下载免费PDF全文
In this paper, we study the Lie symmetrical non-Noether conserved quantity of a holonomic Hamiltonian system under the general infinitesimal transformations of groups. Firstly, we establish the determining equations of Lie symmetry of the system. Secondly, the Lie symmetrical non-Noether conserved quantity of the system is deduced. Finally, an example is given to illustrate the application of the result. 相似文献
14.
Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results. 相似文献
15.
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
16.
Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the non-Noether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results. 相似文献
17.
In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincarè-Chetaev
equations under the general infinitesimal transformations
of Lie groups is discussed. First, we establish the determining
equations of Lie symmetry of the equations. Second, the Lie symmetrical
non-Noether conserved quantity of the equations is deduced. 相似文献
18.
In the present paper the Lie symmetrical non-Noether conserved
quantity of the Poincaré-Chetaev equations of a generalized
classical mechanics under the general infinitesimal transformations
of Lie groups is discussed. First, we establish the determining
equations of Lie symmetry of the equations. Second, the Lie symmetrical
non-Noether conserved quantity of the equations is deduced. Finally,
an example is given to illustrate the application of the results. 相似文献
19.