共查询到20条相似文献,搜索用时 78 毫秒
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研究非保守力和非完整约束对Lagrange系统的Noether对称性的影响. Lagrange系统受到非保守力或非完整约束作用时,系统的Noether对称性和守恒量都会发生变化. 原有的一些Noether对称性消失了,一些新的Noether对称性产生了,在一定条件下,一些Noether对称性仍保持不变. 分别给出系统的Noether对称性以及守恒量保持不变的条件,并举例说明结果的应用.
关键词:
Lagrange系统
非保守力
非完整约束
Noether对称性 相似文献
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研究一类动力学方程的Mei对称性的定义和判据,由Mei对称性通过Noether对称性可找到Noether守恒量.由Mei对称性通过Lie对称性可找到Hojman守恒量.同时,也可找到一类新型守恒量. 相似文献
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研究Hamilton系统的形式不变性即Mei对称性,给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系,寻求系统的守恒量.给出一个例子说明本文结果的应用.
关键词:
Hamilton系统
Mei对称性
Noether对称性
Lie对称性
守恒量 相似文献
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Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod
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In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables: time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals. 相似文献
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A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space–time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete group symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy–momentum conservation law corresponding to the discrete space–time symmetry. A lattice model that respects all local conservation laws and geometric structures is as good as and probably more preferable than standard models on continuous space–time. It can also be viewed as an effective algorithm for the governing differential equations on continuous space–time. 相似文献
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We develop a new cell-centered control volume Lagrangian scheme for solving Euler equations of compressible gas dynamics in cylindrical coordinates. The scheme is designed to be able to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. Unlike many previous area-weighted schemes that possess the spherical symmetry property, our scheme is discretized on the true volume and it can preserve the conservation property for all the conserved variables including density, momentum and total energy. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the performance of the scheme in terms of symmetry, accuracy and non-oscillatory properties. 相似文献
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The symmetries and non-Noether conservation laws of
Birkhoffian system with unilateral constraints are studied. The
differential equations of motion of the system are established,
and the criterions of Noether symmetry, Lie symmetry and Mei
symmetry of the system are given. Two types of new conservation
laws, called the Hojman conservation law and the Mei conservation
law respectively, are obtained, and the intrinsic relations among
the symmetries and the new conservation laws are researched.
At the end of the paper, an example is given to illustrate the
application of the results. 相似文献
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The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres. 相似文献
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Jia-An Lu 《General Relativity and Gravitation》2017,49(11):138
The Poincaré invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance. In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincaré invariant. Actually, the energy–momentum conservation is violated there. On the other hand, with the help of the LIC, the Poincaré invariance is reinterpreted as an internal symmetry. In this formalism, the conservation law is derived, which has not been sufficiently explored before. 相似文献
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Using angle-resolved photoemission we have measured single transitions normal to the surface of Au(111) and identified the same transitions in a family of energy distribution curves obtained from Au(112) and Au(110) at different polar angles. The conservation of the electron momentum parallel to the surfaces makes it possible to locate the transitions in k space along lines of high symmetry without additional assumptions on the final state energy bands. 相似文献
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A. Bhattacharyay 《Physica A》2012,391(4):1111-1119
It is generally believed that sustained directed transport in mechanical systems is not achievable under equilibrium conditions. In this article, by analyzing a simple model, we will show that directed motion under equilibrium conditions can take place and is not inconsistent with conservation of energy and the second law of thermodynamics. Our model demonstrates a novel symmetry breaking mechanism sustainable under equilibrium conditions and average uniform motion of the center of mass is a consequence of the sustained broken symmetry. The most important consequence of our results is that, no current condition for mechanical equilibrium is possibly non-universal. 相似文献
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We propose and implement a quasi-discrete Hankel transform algorithm
based on Dini series expansion (DQDHT) in this paper. By making use
of the property that the zero-order Bessel function derivative
J' 0(0)=0, the DQDHT can be used to calculate the values
on the symmetry axis directly. In addition, except for the truncated
treatment of the input function, no other approximation is made,
thus the DQDHT satisfies the discrete Parseval theorem for energy
conservation, implying that it has a high numerical accuracy.
Further, we have performed several numerical tests. The test results
show that the DQDHT has a very high numerical accuracy and keeps
energy conservation even after thousands of times of repeating
the transform either in a spatial domain or in a frequency domain.
Finally, as an example, we have applied the DQDHT to the nonlinear
propagation of a Gaussian beam through a Kerr medium system with
cylindrical symmetry. The calculated results are found to be in
excellent agreement with those based on the conventional 2D-FFT
algorithm, while the simulation based on the proposed DQDHT takes
much less computing time. 相似文献