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1.
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
2.
Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates 下载免费PDF全文
By introducing the coordination function f, the generalized Mei conserved quantities for the nonholonomic systems in terms of quasi-coordinates are given. Then based on the concept of adiabatic invariant, the perturbation to Mei symmetry and the generalized Mei adiabatic invariants for nonholonomic systems in terms of quasi-coordinates are studied. 相似文献
3.
A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems 下载免费PDF全文
We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico-electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results. 相似文献
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5.
This paper investigates structure equation and Mei conserved quantity
of Mei symmetry of Appell equations for non-Chetaev nonholonomic
systems. Appell equations and differential equations of motion for
non-Chetaev nonholonomic mechanical systems are established. A new
expression of the total derivative of the function with respect to
time $t$ along the trajectory of a curve of the system is obtained,
the definition and the criterion of Mei symmetry of Appell equations
under the infinitesimal transformations of groups are also given. The
expressions of the structure equation and the Mei conserved quantity
of Mei symmetry in the Appell function are obtained. An example is
given to illustrate the application of the results. 相似文献
6.
7.
This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results. 相似文献
8.
Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints 下载免费PDF全文
The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results. 相似文献
9.
XIA Li-Li LI Yuan-Cheng WANG Xian-Jun 《理论物理通讯》2009,51(6):1073-1077
The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results. 相似文献
10.
Mei symmetry and generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints 下载免费PDF全文
This paper studies Mei symmetry which leads to a generalized Hojman
conserved quantity for variable mass systems with unilateral
holonomic constraints. The differential equations of motion for the
systems are established, the definition and criterion of the Mei
symmetry for the systems are given. The necessary and sufficient
condition under which the Mei symmetry is a Lie symmetry for the
systems is obtained and a generalized Hojman conserved quantity
deduced from the Mei symmetry is got. An example is given to
illustrate the application of the results. 相似文献
11.
12.
Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style 下载免费PDF全文
This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results. 相似文献
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14.
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
15.
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry. 相似文献
16.
Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. 相似文献
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18.
The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange-Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results. 相似文献
19.
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