共查询到19条相似文献,搜索用时 95 毫秒
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研究Hamilton系统Noether理论新型的逆问题,得到利用Noether理论从已知的第一积分构建Hamilton函数和对称性的一般解法和若干特殊解法,提出由Hamilton函数直接导出守恒量的两条推论.举例说明所得结果的应用. 相似文献
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从一维减幅-增幅谐振子的运动微分方程出发得到系统的运动积分常数,从而得到系统的Lagrange函数和Hamilton函数,再根据Hamilton函数的形式假定守恒量的形式,由Poisson括号的性质得到了系统的三个守恒量,并讨论与三个守恒量相应的无限小变换的Noether对称性与Lie对称性.还对守恒量与对称性的物理意义作了合理的解释.
关键词:
一维减幅-增幅谐振子
守恒量
Noether对称性
Lie对称性 相似文献
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提出并研究含时滞的非保守系统动力学的Noether对称性与守恒量. 首先,建立含时滞的非保守系统的Hamilton原理,得到含时滞的Lagrange方程;其次,基于含时滞的Hamilton作用量在依赖于广义速度的无限小群变换下的不变性,定义系统的Noether对称变换和准对称变换,建立Noether对称性的判据;最后,研究对称性与守恒量之间的关系,建立含时滞的非保守系统的Noether理论. 文末举例说明结果的应用.
关键词:
时滞系统
非保守力学
Noether对称性
守恒量 相似文献
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本文研究离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量. 构建了离散差分序列变质量Hamilton系统的差分动力学方程, 给出了离散差分序列变质量Hamilton系统差分动力学方程在无限小变 换群下的Lie对称性的确定方程和定义, 得到了离散力学系统Lie对称性导致Noether守恒量的条件及形式, 举例说明结果的应用.
关键词:
离散力学
Hamilton系统
Lie对称性
Noether守恒量 相似文献
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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
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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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The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular
beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the
general solution of transversely isotropic piezoelasticity and Lur’e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface
loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental
equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory.
As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding
equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply
supported piezoelectric beam is examined. 相似文献
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Koki Watanabe Kiyotoshi Yasumoto 《International Journal of Infrared and Millimeter Waves》1999,20(12):2163-2174
A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations. 相似文献
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The problem of deducing one-dimensional theory from two-dimensional theory for a homogeneous isotropic beam is investigated.
Based on elasticity theory, the refined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e
method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and
the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse
surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental
equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory
and are almost the same as the governing equations of Timoshenko beam theory. In two examples, it is shown that the new theory
provides better results than Levinson’s beam theory when compared with those obtained from the linear theory of elasticity. 相似文献
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研究了螺旋线行波管中电子注与高频场互作用的时域理论.电子对场的作用由高频场方程和空间电荷场方程模拟,场对电子注的作用由运动方程模拟.在螺旋导电面模型下利用安培环路定理和法拉第电磁感应定律得到了时域高频场方程.利用空间电荷波模型处理空间电荷场,得到了空间电荷场方程.将高频场和空间电荷场代入洛伦兹力方程,得到了运动方程.利用耦合阻抗处理高频场方程的激励源,使得高频场方程的求解能够借助诸如HFSS或HFCS等高频模拟软件来实现,增强了时域理论的灵活性.基于上述理论,编写软件数值模拟某螺旋线行波管,验证了时域理论的可行性. 相似文献
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In this paper, a Birkhoff--Noether method of solving ordinary
differential equations is presented. The differential equations can
be expressed in terms of Birkhoff's equations. The first integrals
for differential equations can be found by using the Noether theory
for Birkhoffian systems. Two examples are given to illustrate the
application of the method. 相似文献
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Evans attempted to develop a classical unified field theory of gravitation and electromagnetism on the background of a spacetime
obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations.
We now propose a variational principle for a theory that implements some of the ideas that have been (imprecisely) indicated
by Evans and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve
it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation,
together with Evans’ unified field theory, collapses to an ordinary Einstein equation. 相似文献
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In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme confinement, such as nanopores, nanodevices, etc. The approach obtained by combining kinetic and density functional methods is microscopic, fully self-consistent and allows to determine both configurational and flow properties of dense fluids. The theory predicts the correct hydrodynamic behavior and provides a practical and numerical tool to determine how the transport properties are modified when the length scales of the confining channels are comparable with the size of the molecules. The applications range from the dynamics of simple fluids under confinement, to that of neutral binary mixtures and electrolytes where the theory in the limit of slow gradients reproduces the known phenomenological equations such as the Planck-Nernst-Poisson and the Smolochowski equations. The approach here illustrated allows for fast numerical solution of the evolution equations for the one-particle phase-space distributions by means of the weighted density lattice Boltzmann method and is particularly useful when one considers flows in complex geometries. 相似文献
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We present a novel formalism for the generation of integral equations for the distribution functions of fluids. It is based on a cumulant expansion for the free energy. Truncation of the expansion at theKth term and minimization of the resulting approximation leads to equations for the distribution functions up toKth order.The formalism is not limited to systems with two-body interactions and does not require the addition of closure relations to yield a complete set of equations. In fact, it automatically generates superposition approximations, such as the Kirkwood three-body superposition approximation or the Fisher-Kopeliovich four-body one.The conceptual approach is adapted from the cluster variation method of lattice theory. 相似文献