柯尼希定理的实验研究

介绍了刚体平面平行运动中的柯尼希定理的验证实验,并用三种不同形状的刚体验证了柯尼希定理。     

利用刚体的平面平行运动证明平行轴定理

平行轴定理是刚体转动部分的重要知识点,从刚体的平面平行运动模型出发,通过分析刚体运动的总动能的形式,给出了平行轴定理的一种新的证明思路.     

平行轴定理的正确运用

本文通过对一个典型例题的深入分析;指出平行轴定理的应用是有条件的;即只有在刚体绕质心轴转动与绕另一平行轴转动有相同的角速度时;公式才是正确的．     

柯尼希定理运用于两体问题的讨论

本文特别指明,应用柯尼希定理处理系统动能时,首要意义是将系统动能分为系统整体的质心动能和系统内部的有效动能,在这样的认识下运用柯尼希定理,其方法意义才得以充分体现.     

用扭摆验证转动惯量平行轴定理的新方法

提出利用扭摆验证转动惯量平行轴定理的两种简单易行的新方法,并通过实验证明了该方法的可行性.     

扭摆法验证平行轴定理实验的改进

转动惯量是物体定轴转动中的重要物理量,物体的转动惯量测量的常用方法有三线摆法与扭摆法。扭摆法通常测量物体通过质心转轴的转动惯量,所以用扭摆法验证平行轴定理一直不怎么直观,本文就是在已有的基础上进行一些改进,已达到更好、更直观验证平行轴定理。     

转动惯量平行轴定理验证实验的改进方案

本文介绍了一种刚体转动惯量平行轴定理验证实验的改进方案.该方案通过调节对称放置在承物台上的两个钢柱到仪器转轴的距离来改变系统的转动惯量,使得总转动惯量可以在较大的范围内改变,并且始终保持了系统质量的对称性分布,从而有效地减小了实验的相对误差,提高了实验结果的可信度.     

用三线摆研究垂直轴定理

用三线摆对刚体薄圆盘绕不同轴转动时的转动惯量进行测量,通过实验与数据分析,验证了反映刚体转动惯量重要性质的垂直轴定理,从而实现了对刚体转动惯量实验内容的扩充.     

用推广的Maxwell速度分布律证明转动、振动方式能均分定理

将描述分子平动速度分布的Maxwell速度分布律推广到转动和振动方式,并用推广的Maxwell分布律成功地证明了转动、振动方式的能均分定理．     

也谈转动和振动的概率分布与能均分定理的证明

严格推导出分子转动角速度、振动位移概率分布,指明三种概率分布并不局限于近独立子系,它们适用于有相互作用的很多系统。     

Characteristics of Friedel pairs and diffraction contrast tomography with non‐perpendicular rotation axis

The characteristics of Friedel pairs in diffraction contrast tomography (DCT) are studied in the condition that the rotation axis of the sample is not exactly perpendicular to the incident X‐ray direction. For the rotation axis approximately aligned along the vertical direction, the Friedel pairs close to the horizontal plane are insensitive to the non‐perpendicularity of the rotation axis, and can be used to refine the sample‐to‐detector distance and X‐ray energy, while the Friedel pairs close to the vertical direction are sensitive to the non‐perpendicularity of the rotation axis, and can be used to determine the rotation axis orientation. The correct matching proportion of Friedel pairs decreases with increasing non‐perpendicularity of the rotation axis. A method of data processing considering rotation axis misalignment is proposed, which significantly increases the correct matching and indexing proportions of the diffraction spots. A pure aluminium polycrystalline sample is investigated using DCT at beamline 4W1A of Beijing Synchrotron Radiation Facility. Based on the analysis of Friedel pairs, the sample‐to‐detector distance and X‐ray energy are refined to be 8.67 mm and 20.04 keV, respectively. The non‐perpendicular angle of the rotation axis is calculated to be 0.10°. With these refined geometric parameters, the matching proportion of the spatial position of diffraction spots is 90.62%. Three‐dimensional reconstruction of the sample with 13 grains is realised using the algebraic reconstruction technique. It is demonstrated that the precise correction of the orientation of the sample rotation axis is effective in DCT suffering from rotation axis misalignment, and the higher accuracy in determining the rotation axis is expected to improve the reconstruction precision of grains.     

折射定律与反射定律的推导

利用费马原理推导折射定律与反射定律,推导时不需做一些假定(如假定实际光线的光学长度是最小值或折射光线位于入射光线和界面法线所在的平面上),可加深学生对费马原理的理解.     

Experimental evaluation of the claimed coulomb rotation (electrostatic torque)

In the year 2002 publications of A.V.M. Khachatourian and A.O. Wistrom were released, in which the existence of an electrostatic torque has been claimed. This moment of force should act in a three sphere configuration, where one sphere is held at a constant electric potential. This claim was based on an observed rotation and was supported by a mathematical solution derived by Wistrom and Khachatourian. The theoretical work of Wistrom and Khachatourian as well as the interpretation of the observed rotation were criticized by several scientists who offered alternative explanations for the rotation. We therefore designed an experimental setup which enabled us to investigate the phenomenon. By performing numerous measurements, we showed that the rotation is due to asymmetric mass distribution within the sphere, which is dislocated due to electrostatic forces between the spheres. We were able to clear our measurements from this effect and observed a null result more than two orders of magnitude smaller than predicted by Khachatourian and Wistrom's theory. We therefore showed that the rotation doesn't occur in an electrostatic system within the resolution of our experiment.     

关于卡诺定理证明的教学探讨

介绍并讨论了卡诺定理的一种新的证明方法,在这种方法中没有直接使用扳证法,证明过程中的各主要中间结果物理涵义清楚,直观,容易理解。     

Noether's theorem and the fieldB (3)

It is shown that the longitudinal, magnetic flux density,B ⁽³⁾ , of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB ⁽³⁾ to the canonical energy-momentum tensorT _µv that appears in Einstein's field equations of general relativity. Thus,B ⁽³⁾ provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory.     

Thomas rotation and the parametrization of the Lorentz transformation group

Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation axis of a spinning mass, Thomas rotation gives rise to the well-knownThomas precession. A 3×3 parametric, unimodular, orthogonal matrix that represents the Thomas rotation is presented and studied. This matrix representation enables the Lorentz transformation group to be parametrized by two physical observables: the (3-dimensional) relative velocity and orientation between inertial frames. The resulting parametrization of the Lorentz group, in turn, enables the composition of successive Lorentz transformations to be given by parameter composition. This composition is continuously deformed into a corresponding, well-known Galilean transformation composition by letting the speed of light approach infinity. Finally, as an application the Lorentz transformation with given orientation parameter is uniquely expressed in terms of an initial and a final time-like 4-vector.