沟道效应的运动阻尼与系统走向混沌的临界特征

利用正弦平方势,把粒子运动方程化为具有运动阻尼和周期调制的摆方程.利用Melnikov方法分析了系统的全局分叉和混沌行为，指出了沟道辐射本底增强和沟道效应的无规行为与混沌之间的相关性. 关键词： 沟道效应 摆方程 分叉 混沌     

一种适用于双轴旋转式激光陀螺惯导对准的方法研究

为解决舰载惯性导航系统对准时间长的问题,利用分段线性系统理论（PWCS）方法分析了系统的可观测性,并提出了适用于双轴旋转式激光陀螺惯导的多位置对准方案,仿真结果表明该方法在4h内可完成所有陀螺和加速计零位误差的估计,可实现舰栽惯导4h高精度快速对准,具有较好的工程应用价值。     

摆球运动的仿真设计

物体的摆动是自然界最基本的运动形式之一,同时也是力学课程中的基础内容之一.在牛顿力学与拉格朗日力学原理指导下本文利用数学软件Maple强大的计算与图形制作功能对大角度单摆、双摆、有阻力情况下的傅科摆运动问题进行了分析计算,并制作其运动的仿真动画,以精确、生动、形象的动画反映摆球运动的物理规律,实现了可视化教学的目的.     

空竹抛体运动的数值解法和动画模拟

研究了马格努斯效应下的旋转抛体运动,考虑了空气阻力作用于质心上的情况。对于不同初速度和抛出角度,基于Mathematica的计算功能计算得到运动方程的数值解,然后利用软件的可视化功能画出运动轨迹曲线。在Mathematica高版本中还通过控件改变参数,得到动画模拟。使学生更加深入、直观地模拟空竹抛体的运动,同时提高了学习的主动性和创造性。     

The Thomas Precession and the Transformation to Rotating Frames

The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of v/c, important differences in the predicted angle of precession appear, depending on the transformation used. For smaller values of v/c these differences might be measured by extending the time of observation.     

New Perspectives on the Relativistically Rotating Disk and Non-Time-Orthogonal Reference Frames

The rotating disk problem is analyzed on the premise that proper interpretation of experimental evidence leads to the conclusion that the postulates upon which relativity theory is based, particularly the invariance of the speed of light, are not applicable to rotating frames. Different postulates based on the Sagnac experiment are proposed, and from these postulates a new relativistic theory of rotating frames is developed following steps similar to those initially followed by Einstein for rectilinear motion. The resulting theory agrees with all experiments, resolves problems with the traditional approach to the rotating disk, and exhibits both traditionally relativistic and non-relativistic characteristics. Of particular note, no Lorentz contraction exists on the rotating disk circumference, and the disk surface, contrary to the assertions of Einstein and others, is found to be Riemann flat. The variable speed of light found in the Sagnac experiment is then shown to be characteristic of non-time-orthogonal reference frames, of which the rotating frame is one. In addition, the widely accepted postulate for the equivalence of inertial and non-inertial standard rods with zero relative velocity, used liberally in prior rotating disk analyses, is shown to be invalid for such frames. Further, the new theory stands alone in correctly predicting what was heretofore considered a spurious non-null effect on the order of 10^–13 found by Brillet and Hall in the most accurate Michelson-Morley type test to date. The presentation is simple and pedagogic in order to make it accessible to the non-specialist.     

斜入射高速转镜相机数字像面的研究

转镜相机像面设计中,基于传统代替圆理论的设计存在原理性误差,而通过综合考虑几种代替圆理论衍生出来的最佳设计理论会出现圆心不重合、转镜中心点偏离坐标中心等问题,对加工和装配的要求高.在数字像面设计中,把转镜旋转中心点设为坐标中心,推导出每个传感器成像像面坐标和像面边缘离焦量方程,从模拟结果可以看出,转镜扫描时形成了Pascal蜗线,且每个像面又单独为一条直线,符合高速转镜原理和本文计算理论的结论.可为像面定位、工作角、倾斜角选取提供依据.     

Gravitomagnetic Measurement of the Angular Momentum of Celestial Bodies

The asymmetry in the time delay for light rays propagating on opposite sides of a spinning body is analyzed. A frequency shift in the perceived signals is found. A practical procedure is proposed for evidencing the asymmetry, allowing for a measurement of the specific angular momentum of the rotating mass. Orders of magnitude are considered and discussed.     

Effect of Earth's Rotation on the Trajectories of Free-Fall Bodies in Equivalence Principle Experiment

Owing to Earth's rotation a free-fall body would move in an elliptical orbit rather than along a straight line forward to the center of the Earth. In this paper on the basis of the theory for spin-spin coupling between macroscopic rotating bodies we study violation of the equivalence principle from long-distance free-fall experiments by means of a rotating ball and a non-rotating shell. For the free-fall time of 40 s, the difference between the orbits of the two free-fall bodies is of the order of 10-9 cm which could be detected by an SQUID magnetometer because such a magnetometer can be used to measure displacements as small as 10-13 cm.     

激光扫平仪的误差分析与智能检测

分析了激光扫平仪的误差组成及其在等效长焦距检测系统中的三角函数表达式,介绍了检测方法,并给出了实测结果。介绍的等效长焦距智能检测系统不仅能满足不同的精度要求,而且能显著提高检测速度与效率。理论分析和实测结果表明,该仪器的角度测量不确定度优于±2″,角度分辨率优于1″。     

Long-time behavior of the Lorentz electron gas in a constant,uniform electric field

The long-time behavior of the Lorentz electron gas is studied in the presence of a uniform external field. A discussion of the rigorous solution of the one-dimensional Boltzmann equation is followed by the derivation of the asymptotic form of the velocity distribution in an arbitrary number of dimensions. The system is shown to absorb energy from the field without bounds, which excludes the usually assumed steady state with finite thermal energy density.Supported by the Polish Ministry of Higher Education, Science and Technology, Project MR.I.7.The authors are very grateful to Dr. Y. Pomeau for many valuable comments.     

第二类Poeschl-Teller势场中相对论粒子的束缚态

给出了具有第二类Poeschl—Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的8波束缚态解，其解可用超几何函数表示．     

Rosen-Morse势阱中相对论粒子的束缚态

给出了具有Rosen-Morse型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 运用超对称量子力学和形不变性得到了束缚态能谱，通过变量代换求得波函数. 把上述方法推广到相对论量子力学. 关键词： Rosen-Morse势 Klein-Gordon方程 Dirac方程 束缚态     

无反射势阱中相对论粒子的束缚态

给出了具有无反射势型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： 无反射势 Klein-Gordon方程 Dirac方程 束缚态     

Wood-Saxon势中相对论粒子的束缚态

给出了具有Wood-Saxon型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

Weakly Bound Systems in the Case of Complex Potentials

We consider weakly bound two-body systems. We study the behavior of the ground state mean square radius as the binding energy tends to zero in the case of complex potentials. We show that the asymptotic law, obtained with real potentials, is modified by the occurrence of a finite width in the case of finite-range potentials. The case of the PT-symmetric potentials is also discussed. We complete our study with few remarks concerning the same problem for three weakly bound particles.     

在赝自旋对称性势场中运动的相对论粒子的束缚态

在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

General Solutions of Geometric Phase of Neutron in Rotating Magnetic Fields

The exact solutions of the closed evolution of spin states in rotating magnetic fields are described for the most general cases via eigenstate method. A simple algorithm for calculating the geometric phase is exploited.     

旋转锥镜相机研测动态曲率和斜率

采用旋转锥镜相机，进行激光散斑剪切照相，研测缓慢变形物体的动态曲率和斜率。拍摄一张散斑图即可获得曲率和斜率动态变化的全过程。     

相对论情况下赝自旋对称性势场中运动粒子的束缚态

在赝自旋对称性条件下,分别求解了在M rse型和Tan2(πηr)型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.