共查询到18条相似文献,搜索用时 125 毫秒
1.
Hamilton formalism and Noether symmetry for mechanico—electrical systems with fractional derivatives 下载免费PDF全文
This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives.The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established.The definition and the criteria for the fractional generalized Noether quasisymmetry are presented.Furthermore,the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations.An example is presented to illustrate the application of the results. 相似文献
2.
Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems 下载免费PDF全文
This paper investigates the momentum-dependent symmetries for nonholonomic
nonconservative Hamilton canonical systems. The definition and determining
equations of the momentum-dependent symmetries are presented, based on the
invariance of differential equations under infinitesimal transformations
with respect to the generalized coordinates and generalized momentums. The
structure equation and the non-Noether conserved quantities of the systems
are obtained. The inverse issues associated with the momentum-dependent
symmetries are discussed. Finally, an example is discussed to further
illustrate the applications. 相似文献
3.
According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper. 相似文献
4.
This paper discusses the conformal invariance by infinitesimal
transformations of canonical Hamilton systems. The necessary and
sufficient conditions of conformal invariance being Lie symmetrical
simultaneously by the action of infinitesimal transformations are
given. The determining equations of the conformal invariance are
gained. Then the Hojman conserved quantities of conformal invariance
by special infinitesimal transformations are obtained. Finally an
illustrative example is given to verify the results. 相似文献
5.
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results. 相似文献
6.
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
7.
This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equations and restrictive equations and give three definitions of Lie symmetries before the structure equations and conserved quantities of the Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example is presented for illustrating the results. 相似文献
8.
Discrete variational principle and first integrals for Lagrange--Maxwell mechanico-electrical systems 下载免费PDF全文
This paper presents a discrete variational principle and a method to
build first-integrals for finite dimensional Lagrange--Maxwell
mechanico-electrical systems with nonconservative forces and a
dissipation function. The discrete variational principle and the
corresponding Euler--Lagrange equations are derived from a discrete
action associated to these systems. The first-integrals are obtained
by introducing the infinitesimal transformation with respect to the
generalized coordinates and electric quantities of the systems. This
work also extends discrete Noether symmetries to mechanico-electrical
dynamical systems. A practical example is presented to illustrate the
results. 相似文献
9.
Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems 下载免费PDF全文
This paper studies conformal invariance and conserved
quantity of third-order Lagrange equations for non-conserved
mechanical systems. Third-order Lagrange equations, the definition
and a determining equation of conformal invariance of the system are
presented. The conformal factor expression is deduced from conformal
invariance and Lie symmetry. The necessary and sufficient condition
that conformal invariance of the system would have Lie symmetry under
single-parameter infinitesimal transformations is obtained. The
corresponding conserved quantity of conformal invariance is derived
with the aid of a structure equation. Lastly, an example is given to
illustrate the application of the results. 相似文献
10.
Lie symmetry and conserved quantity of a system of first-order differential equations 总被引:5,自引:0,他引:5 下载免费PDF全文
This paper focuses on studying the Lie symmetry and a conserved quantity of
a system of first-order differential equations. The determining equations of
the Lie symmetry for a system of first-order differential equations, from
which a kind of conserved quantity is deduced, are presented. And their
general conclusion is applied to a Hamilton system, a Birkhoff system and a
generalized Hamilton system. Two examples are given to illustrate
the application of the results. 相似文献
11.
Jing-Li Fu Feng-Ping Xie Yong-Xin Guo 《International Journal of Theoretical Physics》2012,51(1):35-48
In this paper, the algebraic structure and the Poisson’s integral theory of f(R) cosmology are presented. Firstly, the Hamilton canonical equations are derived for the system. Secondly, the contravariant
algebraic forms of f(R) cosmology are obtained. Thirdly, the Lie algebraic structure admitted and Poisson’s integral methods are investigated for
f(R) cosmology. Further, the first integrals and solution of f(R) cosmology are given. Finally, an example is given to illustrate the results. 相似文献
12.
The conformal meehanico-electrical systems are presented by infinitesimal point transformations of time and generalized coordinates. The necessary and suflleient conditions that the eonformal meehanieo-eleetrieal systems possess Lie symmetry are given. The Noether conserved quantities of the eonformal meehanieo-eleetrieal systems are obtained from Lie symmetries. 相似文献
13.
Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices 下载免费PDF全文
This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme. This
approach makes it possible to devise techniques for solving the Lagrange--Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone. 相似文献
14.
In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out. 相似文献
15.
16.
We present some features of the smooth structure and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures—it allows us to talk about the canonical structure of differentiable stratified space on the orbispace (an object analogous to a separated stack in algebraic geometry) presented by the proper Lie groupoid. The canonical smooth structure on an orbispace is studied mainly via Spallek’s framework of differentiable spaces, and two alternative frameworks are then presented. For the canonical stratification on an orbispace, we extend the similar theory coming from proper Lie group actions. We make no claim to originality. The goal of these notes is simply to give a complementary exposition to those available and to clarify some subtle points where the literature can sometimes be confusing, even in the classical case of proper Lie group actions. 相似文献
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18.
给出相对论系统的Birkhoff函数和Birkhoff函数组、Pfaff作用量、PfaffBirkhoff原理、Birkhoff方程;研究相对论动力学系统的Birkhoff表示方法;根据在无限小变换下相对论Pfaff作用量的不变性和相对论Birkhoff方程的不变性,得到相对论Birkhoff系统的Noether对称性理论和Lie对称性理论;研究相对论Birkhoff系统的代数结构和Poisson积分方法.
关键词:
相对论
Birkhoff系统
Noether对称性
Lie对称性
代数结构
Poisson积分 相似文献