任意六边形匀质刚板绕垂直板面质心轴的转动惯量公式

提出任意六边形匀质刚板绕垂直板面质心轴的转动惯量的几何方法,并且给出了一些特例的转动惯量公式     

匀质边框三角形刚体绕质心轴的转动惯量公式

确定了任意匀质边框三角形刚体的质心的几何位置;在此基础上推导出匀质边框三角形刚体绕质心轴的转动惯量公式,为计算三角形网格状边框刚体绕质心轴的转动惯量奠定了理论基础.     

任意四边形刚体平板绕质心轴的转动惯量公式

给出了确定任意四边形匀质平板的质心的一种平面几何作图法；并成功地推导出任意四边形刚体平板绕质心轴的转动惯量公式，其特例恰与已知结论相符．     

等腰三角形刚体平板绕质心轴的转动惯量

转动惯量是力学中的一个重要物理量．对于形状为等腰三角形具有对称性的匀质刚体．本文给出了一种求解其绕质心轴的转动惯量的方法．     

对称操作与量纲方法求刚体转动惯量

本文运用对称操作与量纲方法配合平行轴定理推导出非对称的任意三角形平板及平行四边形平板绕质心轴的转动惯量公式，从而避免了繁杂的积分．其特例正好是文献［１］的结果     

匀质三角形板和边框的转动惯量

质量均匀分布的物体相对质心轴的转动惯量,通常是由它的几何量表示,这称为转动惯量的几何表示．如果给定物体的顶点坐标,它相对任意轴的转动惯量可以由这些顶点坐标表示,这称为转动惯量的代数表示．由转动惯量的平行轴定理,得到杆和三角形板相对任意转轴转动惯量的代数表示．作为简单应用,得到三角形边框相对质心轴转动惯量的几何量表示．     

对称操作与量纲方法求刚体转动惯量

本文运用对称操作与量纲方法配合平行轴定理推广导出非对称的任意三角形平板及平行四边形平板绕质心轴的转动惯量公式，从而避免了繁杂的积分，其特征正是文献（１）的结果。     

任意四边形刚体平板绕质心轴的转动惯量公式

本文给出了任意四边形刚体平板绕其质心轴的转动惯量公式，并在极限情形及对称条件下给出若干推论；均与已知结果相吻合。     

刚体绕任意轴转动惯量的简便计算

利用微元求和的方法给出几种刚体对于过质心任意轴的转动惯量公式，并由此引出转动惯量与刚体几何对称性的联系，以及与转动惯量有关的几何形体等价性的一些结果．     

刚体绕任意轴转动惯量的简便计算

利用微元求和的方法给出几种刚体对于过质心任意轴的转动惯量公式，并由此引出转动惯量与刚体几何对称性的联系，以及与转动惯量有关的几何形体等价性的一些结果。     

Electromagnetic waves in uniaxial crystals with metallized boundaries: Mode conversion,pure reflections,and bulk polaritons

A theory is constructed for the reflection of plane electromagnetic waves in uniaxial crystals with a positive definite permittivity tensor and an arbitrarily oriented metallized boundary. The problem is solved both for general-position orientations corresponding to three-partial reflection and for special conditions allowing two-partial reflections: mode conversions when the incident and reflected waves belong to different sheets of the refraction surface and “pure” reflections when both waves belong to the same sheet. The space of pure reflections is shown to be formed by two types of optical-axis orientations: arbitrary directions in the plane of the crystal surface and in the plane of incidence. The configurations of the conversion surface for optically positive and negative crystals are investigated. A subspace of pure reflections that transform into one-partial bulk polaritons with the energy flux parallel to the surface at grazing incidence has been found. The domain of existence of such bulk eigenmodes is bounded by two “lines” of solutions. These are any directions along the boundary containing the optical axis for ordinary polaritons and the direction along the projection of the optical axis onto the surface at an arbitrary orientation of the axis with respect to the boundary for extraordinary polaritons.     

Focusing of electromagnetic waves into a uniaxial crystal

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal. To that end we start from existing exact solutions for the transmitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we specialize to the case in which the medium of the incident wave is isotropic and derive explicit expressions for the dyadic Green's functions associated with the transmitted fields as well as integral representations suitable for asymptotic analysis and efficient numerical evaluation. Relevant integral representations for focused 3D electromagnetic waves are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem, and derive dyadic Green's functions, integral representations suitable for asymptotic and numerical treatment, and integral representations for focused TM fields. Numerical results for focused 2D TM fields based on these integral representations as well as corresponding experimental results will be presented in forthcoming papers.     

周视大像旋稳海天线向量角补偿算法

为使两轴周视光电探测系统在三自由度扰动和大像旋条件下搜索并跟踪水面目标,在虚拟天际线焦平面像五自由度解析表达式基础上,推导出焦平面坐标系铅直轴的方向向量和该坐标系下海天出射平面法向量夹角的余弦表达式.该式求反余弦后减π/2,得到焦平面铅直坐标轴的方向向量和海天出射平面法向量小于π/2的夹角,该夹角的0.5倍作为俯仰反射镜的净作动量,目的是克服非线性像旋使包含目标信息的虚拟海天线的像线通过焦平面中心.该算法与方位补偿算法联动能够使目标像点始终逼近焦平面原点.通过数学模型仿真和真实工况试验都验证了俯仰机构位置环海天线向量角补偿算法的合理性.     

圆电流空间磁场分布

在柱坐标系中,直接从磁感应强度的计算公式毕奥一萨伐尔定律出发,在更为普遍的情况下得到了圆电流空间磁场的一般分布,并绘制出磁场的空间分布图,讨论了圆电流平面上、中心轴线以及远区的磁场．     

Optimal length of an electro-optical Q-switch with optical activity crystal La3Ga5SiO14

With the polarization plane gyration and the electro-optic effect existing simultaneously in an optical activity crystal, the theory on interaction of optical activity and electro-optic effect on the arbitrary linearly polarized light propagating through the crystal along the optical axis is studied. The electro-optical Q-switch is designed successfully. With the conclusion of the theory, the optimal length of optical activity crystal using as electro-optical Q-switch at a given wavelength is calculated.     

States of cobalt fluoride in a strong magnetic field

The behavior of the magnetic subsystem of cobalt fluoride is investigated in a strong magnetic field oriented in an arbitrary direction in space. In the case where the magnetic field is out of the planes passing through the easiest magnetization axis A and the axis [100] ‖ X or through the easiest magnetization axis A and the axis [010] ‖ Y, it follows from the derived system of equations that the antiferromagnetic vector l does not change direction to be align with the basal plane, provided the magnetic field has a nonzero component along the A axis. It is demonstrated that the antiferromagnetic vector l becomes parallel to the basal plane only when the magnetic field is perpendicular to the A axis. The case of the magnetic field directed parallel to the [110] axis is examined thoroughly. The critical value of the magnetic field is determined at which the antiferromagnetic vector l becomes parallel to the basal plane and perpendicular to the external magnetic field H for H _⊥ → ∞.     

Effects of optical axis direction on optical path difference and lateral displacement of Savart polariscope

A simple method is applied to calculating the optical path difference (OPD) of a plane parallel uniaxial plate with an arbitrary optical axis direction. Then, the theoretical expressions of the OPD and lateral displacement (LD) of Savart polariscope under non-ideal conditions are obtained exactly. The variations of OPD and LD are simulated, and some important conclusions are obtained when the optical axis directions have an identical tolerance of \pm 1^{{\circ}}. An application example is given that the tolerances of optical axis directions are gained according to the spectral resolution tolerances of the stationary polarization interference imaging spectrometer (SPIIS). Several approximate formulae are obtained for explaining some conclusions above. The work provides a theoretical guidance for the optic design, crystal processing, installation and debugging, data analysis and spectral reconstruction of the SPIIS.     

Generalized ellipsometry of anisotropic media

The determination of the parameters of an arbitrary reflection matrix of a medium using PCSA null ellipsometry with a fixed compensator is considered. The ordinary four-zone scheme of measurements is shown to have limited capabilities of determining the matrix components. Additional measurements in the Kerr zones for the compensator axis oriented parallel to the plane of incidence or reflection extends the capabilities of the method and allows the problem to be solved completely in the case of small off-diagonal components.