轴对称可压缩流的统一坐标系

将Hui等人提出的统一坐标系推广到轴对称欧拉方程,讨论统一坐标系下的轴对称欧拉方程的解法,并通过数值算例证明轴对称统一坐标系的优越性.     

对气象常用坐标系中位涡形式的探讨

气象常用垂直坐标系中的位涡方程及位涡形式是位涡理论及位涡诊断技术的基础.本文依据坐标转换的观点,分别用两种不同的方法推导出等压坐标和等熵坐标中的位涡方程及相应的位涡表达式.一是从三维矢量运动方程出发,由三维涡度方程、连续方程和热力学方程推导位涡方程;二是直接从等压坐标和等熵坐标中的标量运动方程组出发推导位涡方程.结果表明,用两种方法所得到的等压坐标中的位涡方程和位涡表达式形式有所不同,而等熵坐标中用两种方法所得到的位涡方程和位涡形式相同.对垂直坐标系的物理本质分析表明,采用第一种方法时尽管矢量运动方程中的 关键词： 位涡 坐标转换 等压坐标 等熵坐标     

理论力学自学辅导材料(三)——非惯性系内质点力学

非惯性系内质点力学主要包括三方面内容:一、两坐标系间速度和加速度的变换关系.它起着桥梁的作用,有了它就能从已知的质点相对于惯性系的运动规律推导出质点相对于非惯性系的运动规律.其中不需要附加任何新的假设.另一方面它是质点运动学理论的一部分,为分析研究比较复杂的质点运动提供了一种很有用的简化方法.二、在非惯性系内质点的动力学方程.它是解决非惯性内质点动力学问题的出发点.三、由地球自转产生的一些重要现象.本文仅就一、二两方面作一些说明.一、两个坐标系间速度和加速度的变换关系 为了掌握这两个变换关系的推导,应搞清以…     

斜置偶极子场强具体表达式的另一种求法

基于电偶极子场强的矢量表达式,应用坐标系转换关系,推导出斜置电偶极子场强在笛卡尔坐标系、球面坐标系和柱面坐标系中的具体表达式。     

平面运动学的欧拉公式描述和分析

针对平面运动学相关问题,采用复函数平面代替传统的Oxy坐标系的实数平面并引入以复指数形式表达的欧拉公式,进行描述和分析,避免了传统的实数平面矢量分析中点积和叉积运算规则所带来的困惑以及繁琐的矢量分析.并引入了瞬时坐标系,其结论与经典理论完全一致.     

机载光电系统的目标定位研究

为了解决光电系统的目标定位问题,提出了一种机载光电系统的自主定位方法.利用齐次坐标变换方法推导了机载光电目标从光电平台极坐标系到WGS-84大地坐标系的转换方程;采用工程实例进行了机载光电系统的目标定位误差分析.分析结果表明,该方法可以减小定位误差,获得较高的定位精度,满足对海上或陆上目标定位的需求.该方法实现简单,具...     

刚体一般运动的描述

刚体的一般运动是刚体运动学中最复杂的一类运动,其求解通常需要借助欧拉定理或沙勒定理.通过这两个定理,我们可以把刚体的一般运动分解成较简单的定轴转动和平动.本文主要应用代数理论中的正交矩阵描述刚体的运动,并用代数语言分析了定点转动的本征问题,证明了欧拉定理.随后,将刚体的定点转动进行分解,并给出了物理图像和推导结论,完成...     

与月球有关的引潮力

从简化的地月系统力学模型出发,严格推导出地表物体动力学方程在转动坐标系下的表示形式,通过对称性的分析,得到引潮力,从而有助于加深对引潮力和潮汐成因的理解.     

二维高斯波束对多层球粒子电磁散射的解析解

基于矢量波函数在球和柱坐标系中表达式之间的转换关系，提出了一种求解球坐标系中二维高斯波束波形因子的方法，得到了二维高斯波束波形因子在球坐标系中的解析公式.结合广义米理论推导了在轴二维高斯波束入射多层球粒子的电磁散射的解析解，并对散射强度随散射角的分布进行了数值模拟，结果与平面波入射情况进行了比较.     

球面平均值函数及其微分方程的推导

三维波动方程初值问题是数学物理方法课程的重要教学内容.本文讨论球面平均法求解该问题时,球面平均值的定义及其满足的偏微分方程的建立过程.在教材常见推导的基础上,本文提出了球面平均值方程一种更简洁的推导方法.本文的讨论有利于澄清球面平均值函数的含义,为球面平均法以及球坐标系下数学物理方程的教学提供参考.     

The form-invariance of wave equations without requiring a priori relations between field variables

According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.     

The use of polarized coordinates for solving the macroscopic equations of collisionless plasma

A method is developed for the iterative solution of an infinite system of moment equations derived from the collisionless Boltzmann (Vlasov) equation. Since in a strong magnetic field the dominant terms of these equations have a complicated form, the iterative solution after a few steps comes up against difficulties connected with the inversion of matrices of high order. It is found that the transformation of moment equations into the natural polarized coordinate system (Buneman O.: Phys. Fluids4 (1961), 669) diagonalizes the dominant matrices in the magnetic fields with straight lines of force exactly and in adiabatic magnetic fields approximately. In addition, this transformation reveals the symmetries of the moment equations which in some cases permit an exact solution to be found. Apart from the first three moment equations (the equation of continuity, the dynamic (Euler) equation, the equation for pressure) the general moment equation of then-th order is also derived in the Cartesian and general curvilinear coordinate system and in the corresponding polarized natural coordinate systems. The paper deals with some special cases of natural polarized coordinate systems belonging to a magnetic field with straight lines of force (plane, cylindrical and spherical geometry) and with curved lines of force (magnetic trap with mirrors).     

On the definition of the natural frequency of oscillations in nonlinear large rotation problems

Computational multibody system algorithms allow for performing eigenvalue analysis at different time points during the simulation to study the system stability. The nonlinear equations of motion are linearized at these time points, and the resulting linear equations are used to determine the eigenvalues and eigenvectors of the system. In the case of linear systems, the system eigenvalues remain the same under a constant coordinate transformation; and zero eigenvalues are always associated with rigid body modes, while nonzero eigenvalues are associated with non-rigid body motion. These results, however, cannot in general be applied to nonlinear multibody systems as demonstrated in this paper. Different sets of large rotation parameters lead to different forms of the nonlinear and linearized equations of motion, making it necessary to have a correct interpretation of the obtained eigenvalue solution. As shown in this investigation, the frequencies associated with different sets of orientation parameters can differ significantly, and rigid body motion can be associated with non-zero oscillation frequencies, depending on the coordinates used. In order to demonstrate this fact, the multibody system motion equations associated with the system degrees of freedom are presented and linearized. The resulting linear equations are used to define an eigevalue problem using the state space representation in order to account for general damping that characterizes multibody system applications. In order to demonstrate the significant differences between the eigenvalue solutions associated with two different sets of orientation parameters, a simple rotating disk example is considered in this study. The equations of motion of this simple example are formulated using Euler angles, Euler parameters and Rodriguez parameters. The results presented in this study demonstrate that the frequencies obtained using computational multibody system algorithms should not in general be interpreted as the system natural frequencies, but as the frequencies of the oscillations of the coordinates used to describe the motion of the system.     

均匀磁场中二维各向同性带电谐振子的守恒量与对称性研究

由牛顿第二定律得到二维各向同性带电谐振子在均匀磁场中运动的运动微分方程,通过对运动微分方程的直接积分得到系统的两个积分(守恒量).利用Legendre变换建立守恒量与Lagrange函数间的关系,从而求得系统的Lagrange函数,并讨论与守恒量相应的无限小变换的Noether对称性与Lie对称性,最后求得系统的运动学方程.     

Conformally Invariant Generalization of Einstein Equations and the Causality Principle

The paper presents an improved derivation of the dynamic equations for the conformally invariant generalization of Einstein's equations. The consistency of the variational procedure with the causality principle is studied. The well-posedness of the Cauchy problem in the synchronous coordinate system is proved as applied to the generalized equations. The possibility of generalized equations at finding quantitative relations between observed values is noted.     

Scattering of shaped beam by an arbitrarily oriented spheroid having layers with non-confocal boundaries

An approach to express an incident shaped beam with respect to an arbitrarily oriented spheroidal particle having layers with non-confocal boundaries is presented. To overcome the difficulty of non-confocal boundary conditions connected with different spheroidal coordinate systems, a theoretical procedure is developed to deal with the non-confocal boundary conditions by virtue of a transformation for vector wave functions. The unknown coefficients of scattered and internal electromagnetic fields are determined by solving a system of linear equations derived from the boundary conditions and relations between the spheroidal vector wave functions and spherical ones. Numerical results of the normalized scattering cross section for a two-layered non-confocal prolate spheroid are evaluated. PACS 42.25.Fx; 42.25.Bs     

Bracket formulation of dissipative fluid mechanics equations

The bracket formulation of the Euler fluid mechanics equations is extended to the fluid mechanics equations corresponding to the Navier-Stokes-Fourier and the Edelen constitutive relations.     

Equivalence and gauge in the Planck-scale aether model

Following the 19th century program by Dirichlet, Helmholtz, Thomson, and Hertz to obtain a completely kinematic interpretation of classical mechanics by the nonlinear Euler equations, an attempt is made to interpret the gauge and equivalence principles hydrodynamically in the framework of the Planck aether model.