共查询到19条相似文献,搜索用时 62 毫秒
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利用d’AlembertLagrange原理的Chaplygin形式在无限小变换下的变形形式得到Chaplygin系统的广义Noether等式和守恒量的形式.研究Chaplygin系统的形式不变性以及它与Noether对称性的关系.
关键词:
Chaplygin系统
Noether对称性
形式不变性
守恒量 相似文献
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研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整系统形式不变性的定义和判据,得到形式不变性的结构方程和守恒量的形式,并举例说明结果的应用.
关键词:
相空间
二阶线性非完整系统
形式不变性
守恒量 相似文献
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从拉格朗日函数的不确定性出发,通过作为积分上发的坐标函娄之作用量S=∫tt1Ldt′=S(x^μ)及其不确定性,得到ψ与ψ′=e^-iqa(x^μ)ψ等效-定域规范不变性或日局域对称性。 相似文献
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利用一种直接方法将阻尼谐振动微分方程变换成等价的自伴随形式,并构造出阻尼振子的两个拉格朗日函数和哈密顿函数,导出了阻尼谐振子的Noether守恒量. 相似文献
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给出转动相对论系统的Appell方程,讨论相对论力学的四个新型基本动力学函数 在无限小群变换下研究转动相对论系统Appell方程的形式不变性,给出定义和判据 研究形式不变性与Noether对称性与Lie对称性的关系,寻求转动相对论系统的守恒量
关键词:
转动相对论 Appell方程 形式不变性 对称性与守恒量 相似文献
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This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. Ac-cording to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and estab-lishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is giver to illustrate the application of the results. 相似文献
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In this paper,we study the relation between the form invariance and Lie symmetry of non-holonomic systems.Firstly,we give the definitions and criteria of the form invariance and Lie symmetry in the systems.Next,their relation is deduced.We show that the structure equation and conserved quantity of the form invariance and Lie symmetry of non-holonomic systems have the same form.Finally,we give an example to illustrate the application of the result. 相似文献
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In this paper, the differential equations of motion of a three-body interacting pairwise by inverse cubic forces(“centrifugal potential”) in addition to linear forces (“harmonical potential”) are expressed in Ermakov formalism in two-dimension polar coordinates, and the Ermakov invariant is obtained. By rescaling of the time variable and the space coordinates, the parametric orbits of the three bodies are expressed in terms of relative energy H1 and Ermakov invariant. The form invariance of the transformations of two conserved quantities are also studied. 相似文献
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研究单面完整约束力学系统的形式不变性.根据运动微分方程的形式在无限小变换下的不变性,给出了单面完整约束力学系统形式不变性的定义和判据,建立了系统的形式不变性与Noether对称性、Lie对称性之间的关系,并举例说明结果的应用.
关键词:
分析力学
单面约束
形式不变性
Lie对称性
Noether对称性
守恒量 相似文献
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Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations 下载免费PDF全文
This paper studies the conformal invariance by infinitesimal point
transformations of non-conservative Lagrange systems. It gives the
necessary and sufficient conditions of conformal invariance by the
action of infinitesimal point transformations being Lie symmetric
simultaneously. Then the Noether conserved quantities of conformal
invariance are obtained. Finally an illustrative example is given to
verify the results. 相似文献
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Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices 下载免费PDF全文
The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results. 相似文献