科里奥利力产生的物理分析

在匀速转动参考系中,质点以匀速运动时,则有科氏力作用于质点上.从加速度基本定义出发,利用矢量进行分析,不仅能很容易得出科氏力,而且能清楚地看出其物理意义.现仅就下面两种特定情况加以讨论. (一)质点沿转动圆盘半径方向作匀速直线运动. 设圆盘相对于惯性系统以匀角速度绕轴转动,质点以匀速v’沿圆盘上的矢径(OP)作直线运动.(图1).大家知道,在转动参考系中,要保持质点作匀速直线运动,必须对质点施以真实力F,以抵消惯性力的作用。亦即有由于真实力与坐标系无关,它在惯性参考系中为F=ma,式中a为相对于惯性参考系的加速度.显然,求出加速度…     

第六章 曲线运动 万有引力定律

第六章曲线运动万有引力定律练习一运动叠加原理平抛运动匀速圆周运动一、判断题１．质点在平面上的任意运动，都可以看成是两个相互垂直的直线运动的叠加。（）２．平抛运动是加速度不变的运动。（）３．钟表秒针尖端做匀速圆周运动的周期为１ｓ。（）４．当砂轮转速一定...     

匀速运动的均匀带电细圆环轴线上的电场

静电场教学中多数是研究静止不动的带电体所产生的电场,在强调静止的同时,学生会自然想到"静止"是相对的,"运动"是绝对的,运动的带电体其电场又是如何分布的?本文就讨论做匀速直线运动的均匀带电细圆环其轴线上的电场分布情况.     

匀速直线运动的带电圆环轴线上的电场和磁场

本文利用相对论变换关系计算了沿轴线方向匀速直线运动的带电圆环轴线上的电场和磁场．     

匀速直线运动为背景的问题赏析

匀速直线运动是最简单的运动形式,但涉及到几个物体同时做匀速直线运动时,问题也并不简单. 例1:一支长为150m队伍匀速前进,通讯兵从队尾赶到队前传达命令即返回,当通讯兵回到队尾时,队伍已前进了200m,则通讯兵走过的路程为m. 析与解:这儿队伍和通讯兵都是做匀速直线运动,通讯兵从队伍的尾部赶到队前,又从队前赶到队尾,和队伍之间可以看成追赶、相遇问题. 设通讯兵的速度大小为v1,队伍前进的速度大小为v2,通讯兵从队尾赶到队前用时t1,从队前回到队尾用时t2.     

两种“等时圆”模型

如能巧妙地将某些特殊运动的时间问题转换成几何圆模型中的几何弦问题来处理,会达到柳暗花明的效果,是一种行之有效的途径.下面介绍两种"等时圆",一种是光匀速直线运动的问题,另一种是初速度为零的匀加速直线运动的问题.     

质点沿最速降线和首尾固定的两相连线段下落问题的研究

目前关于最速降线即圆滚线的由来原理的文章有不少,但多数是直接套用光学折射定律进行类比推理,缺少对方法原委的详细介绍和对运动细节的探讨,或者仅是局部的数值计算而缺乏物理内涵.至于与圆滚线存在关联的质点沿首尾固定的两相连直线段降落的时间这样更为基础的问题,却少有人撰文研究.本文首先推导出质点速降问题中的"折射定律",然后利用它推导出最速降线即圆滚线的方程.证明了质点沿圆滚线的速降运动等价于匀速滚动圆周上对应点的绝对运动.给出最速降运动方程和计算圆滚线具体参量及质点降落时间的方法,并举例说明.指出当降落终点处在圆滚线左右半拱时,圆滚线参量的计算公式有所区别.简单地论证了圆滚线是唯一的捷线.最后,通过求极值的方法,计算出首尾固定的两相连直线段的最速降折点位置,以及在纵、横坐标给定时的最速降折点位置.通过列表和作图,分析出降落时间随折点的变化规律.     

导出卢瑟福公式的简易方法

卢瑟福公式在《理论力学》教材中一般是从比耐公式出发导出来的,过程比较复杂.现介绍一个用动量矩(角动量)守恒律来导出卢瑟福公式,方法比较简单.-a质点运动的性质 把一个a质点射入原子中,因为a质点带电荷2e,原子核带正电荷2e,(Z为原子的原子序数)它们相互作用遵循库仑定律斥力:又因原子核的质量一般比a质点的质量大许多倍,故近似的可以认为原子核不动,所以a质点运动的性质,是在平方反比斥力的有心力的作用下的运动问题.a质点的轨道是双曲线的一支,这时力心(原子核)在轨道凸的一边.二示意图说明 如图:o代表原子核(力心)的位置,设a质点在力…     

基于相位相关的匀速直线运动模糊图像位移参数估计

为估算匀速直线运动模糊图像的运动参数,提出了一种基于相位相关分析的图像配准方法。该方法利用傅里叶变换的平移特性,对产生平移的目标图像进行傅里叶变换并计算归一化互功率谱,其傅里叶逆变换对应二维脉冲函数,通过计算脉冲函数峰值坐标获取位移图像之间的亚像元级位移量。结合相位相关配准原理和线性空间不变退化模型,给出了匀速直线运动点扩散函数及其光学传递函数的数学描述;讨论了匀速直线运动模糊对相位相关配准结果的影响,证明了图像经过匀速直线运动退化后,位移图像之间归一化互功率谱具有不变性。实验结果表明：动态运动模糊图像最大检测误差为0.489 pixel,标准差为0.16 pixel。     

自感和互感

电磁感应的两种类型第一种类型我们知道当带电体在磁场中运动时,它会受到一个力,叫做洛仑茲力。例如一个带电质点在均匀磁场中运动时,如果它原来的速度与磁场垂直,那么它受洛仑茲力作用的结果就会作圆周运动;如果原来速度与磁场平行那么洛仑茲力为零,带电质点就直线等速前进;如果原来速度与磁场有一任意倾斜角,则质点将作螺旋式的运动。值得注意的是,无论哪种情况质点速率都不变,也就是说洛仑茲力并不对质点作功,因此不能使质点获得能量,而只能影响质点运动的方向。现在来考察一根导线在磁场中运动的情况。为简单计假定磁场方向、导线和运动方向互相垂直。这时导线中的自由电子,象上述带电质点一样,因为受到洛仑茲力,就有作圆周运动的趋势,但由于导线对于电子     

PIV measurement of toner particle motion in a micro-gap in the development process of electrophotography

In the development process of electrophotography, charged dielectric toner particles move in a micro-gap between the photoreceptor and the development roller to form images by the action of electrostatic force. To improve image quality, it is important to clarify the toner particle motion and the effects of the electric field on this motion. In the present study, Particle Image Velocimetry (PIV) was applied to measure the toner particle motion and the results were compared to calculated results. It was confirmed that the toner velocity increased with increasing electric field intensity, and that the measurement results agreed with the calculated results. These results indicated the usefulness of PIV in analyzing toner particle motion in the development process.     

A Charged Particle in an Electric Field in the Probability Representation of Quantum Mechanics

The Green's function and linear integrals of motion for a charged particle moving in an electric field are discussed. The Wigner functions and tomograms of the stationary states of the charged particle are obtained. The relationship between the quantum propagators for the Schrödinger evolution equation, the Moyal evolution equation, and the evolution equation in the tomographic-probability representation for a charged particle moving in an electric field is discussed.     

带电粒子在正交电场和磁场中轨迹的形成及曲率半径

本文讨论了带电粒子在正交的电场和磁场中于不同条件下的旋轮线轨迹,并讨论了这些不同形状的旋轮线是怎样由圆轮的纯滚动形成的,使带电粒子的运动过程更加直观,并且运用物理方法导出了旋轮线曲率半径的普遍公式.     

E2》H2的均匀正交电磁场中带电粒子的相对论运动

通过求解带电粒子在均匀电场中与坐标系选取无关的三维矢量相对论运动方程,进而利用洛伦兹变换方法,求得了带电粒子在E2>H2的均匀正交电磁场中相对论运动轨迹的一般三维矢量式.并使用Mathematica软件在直角坐标系中描绘了相应的粒子相对论运动轨迹图.     

Electric Chern–Simons term, enlarged exotic Galilei symmetry and noncommutative plane

The extended exotic planar model for a charged particle is constructed. It includes a Chern–Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern–Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons.     

Exact solution to the classical equation of motion for a charged particle in external electric and magnetic fields

An exact solution to the equation of classical motion of a charged particle in external uniform time-dependent electric and magnetic fields is obtained in two forms by two methods. An exact solution of a more general initial-value problem is found as well.     

The Larmor nutation

The classical non-relativistic problem of the motion of a charged particle in an external central force field and a weak uniform magnetic field is revisited to show that the motion of the kinetic angular momentumL = r × p of the particle, in the so-called Larmor approximation, is not a simple precession but is actually a composite motion involving precession as well as a high frequency nutation. The precession-nutation motion ofL is discussed in the Larmor approximation when the Larmor-frame-orbit of the charged particle is an ellipse (or a circle) for the case of the two central forces namely the Coulomb and the Hooke-law-force, which are the only two central forces known to permit closed orbits.     

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schrödinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schrödinger equation and some special and limiting cases are outlined.     

Motion of a Charged Particle in an Arbitrary Time-Dependent Electric Field with Alternating Intersite Interactions

The motion of a charged particle on a linear chain under the action of an electric field with alternating intersi te interactions is investigated. Exact solutions for the Wannier state amplitudes, the propagators and the mean square displacement are obtained for the general case of an arbitrary time-dependent electric field, of which a dc+ac electric field is only a special one. The dynamic localization condition is given for this special case. This condition would make the observation of dynamic localization effect possible.     

An approximate calculation of the non-adiabatic motion of a charged particle in an inhomogeneous rotationally symmetric magnetic field

A study is made of the motion of a particle injected longitudinally into a rotationally symmetric magnetic field increasing linearly in an arbitrarily sharp way on the axis of symmetry. By expanding the magnetic potential in a series in the vicinity of the line of force from which the particle starts, and by restricting our considerations to linear terms, we arrive at a single linearized equation of motion for the radial motion, as we assume the longitudinal motion to be uniform. The linearized equation can be solved exactly. Numerical evaluation is carried out (with the linearized line of force) for several different slopes of the field, and compared for similar cases with a numerical evaluation of an exact nonlinear problem. The method described in the paper can also be applied to cases with more general initial conditions, when the particle also moves with an azimuthal velocity.The author extends his thanks for valuable advice, discussions and encouragement to Dr. M. Seidl, on whose incentive the work was undertaken and who is the author of equation (13).