分析力学中单摆模型广义坐标选取的任意性分析

分析力学中单摆模型的广义坐标若选取为竖直方向高度,则存在＂矛盾＂,貌似破坏了广义坐标选取的任意性,本文针对此问题进行了分析,并提出了两种修正后的广义坐标选取方案来解决此＂矛盾＂,从而说明在单摆模型中广义坐标选取的任意性没有被破坏.     

用单摆测重力加速度实验中单摆周期的测定

对用单摆测重力加速度实验中单摆周期的测定进行了研究,给出了一种基于电子秒表的自动测量单摆周期的可靠装置,改进了传统单摆周期测量的不足,提高了测量单摆周期的精度.     

用微元法推导无阻尼单摆运动任意角度下的周期公式

对单摆运动进行了讨论。通过对单摆进行能量分析,得出了单摆角频率与角度的关系式,然后运用微元法,推导出了单摆的理论周期公式。计算结果表明,所得到的单摆运动周期的理论公式与展开公式符合得很好。     

自制单摆振动图像描绘实验仪

为获得简谐运动的清晰图像,自制了单摆振动图像描绘实验仪.实验将带有放电针的单摆与高压脉冲的电极相连,在单摆下方放置一匀速运动的纸带,当单摆振动时,由尖端放电原理可知,在纸带上将描绘出单摆振动的图像.     

大学物理教学中对大角度单摆的介绍

大学物理的教学在简谐振动部分介绍了小角度单摆,但没有介绍摆角较大时单摆的运动.利用Matlab研究了大角度的单摆运动,得到了大角度单摆的运动曲线,曲线表明,尽管摆角较大时单摆不再做简谐振动,但其运动曲线看似余弦曲线,且具有一定的周期性;文章给出了小角度单摆的相图及其与实际摆动的对比动画;对大角度单摆运动的相图进行了分析,说明在摆角较大时单摆的运动将不同于简谐振动而更加复杂.在此基础上,探讨了如何把所得结论引入到大学物理教学中,以加深和拓展学生对单摆运动的理解.     

基于LabVIEW的单摆振动图像的探究实验

针对传统实验的不足,结合数据采集和虚拟仪器测量技术,开发了基于LabVIEW的单摆振动图像的探究实验装置,实现了单摆振动图像的绘制、单摆周期的测量和当地重力加速度的计算,直观地展示了单摆振动图像,提高了可视化效果和测量精度,降低操作难度,并将单摆振动图像演示实验和用单摆测定重力加速度实验进行了整合,提高了测量效率.     

单摆周期公式的讨论

学生对单摆周期公式T=2π／L/g都能理解，但对“变形单摆”问题感到束手无策．本文就“单摆的摆长”和单摆的“等效重力加速度”做一阐述，从而导求出运用单摆周期公式T=2π／L/g的一般规律．     

单摆运动的实时测量

对传统单摆装置进行改进,在摆球上安装小金属探针,用软导线做摆线,在单摆下方放置带电水槽,使单摆摆动时探针在水面划动,将振动量转化为电位量,实现了单摆振动的实时测量.     

单摆的振动图像演示装置

用电火花计时器作单摆的高压电源,使单摆的针尖和铜片间产生火花放电,并且在单放机带动而做匀速直线运动的纸带上产生放电点迹,形成单摆的振动图像.根据振动图像探究单摆的振动周期与振幅、摆长和摆的质量是否有关.     

磁单摆的系列振动演示实验

磁单摆的系列振动演示实验复旦大学物理系刘贵兴，童培雄单摆振动与弹簧振子的振动一样，都是属于典型的简谐振动．以往演示单摆振动的实验内容较少．为了弥补这方面的不足，本文介绍用一只由铝镍钻制成的强磁性的圆柱形磁钢作为普通单摆的摆锤（我们称其为磁单摆，以下简...     

On the Possibility to Construct Gravitational Eye

The possibility of modifying a conventional Cavendish torsion pendulum into a half-armed pendulum oscillator to measure the horizontal gravitational acceleration is discussed. A new kind of gravitational detector, gravieye, as we named, can be made by a proper combination of such oscillators to ＂see＂ remote objects and to be used, e.g. to detect the movement of huge mass at a long distance.     

Collective dynamics in a non-dissipative two-coupled pendulum system

We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization （PS） and measure synchronization （MS）. We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Fu~.hermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincar6 sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.     

Physical analysis on improving the recovery accuracy of the Earth’s gravity field by a combination of satellite observations in along-track and cross-track directions

The physical investigations on the accuracy improvement to the measurement of the Earth＇s gravity field recovery are carried out based on the next-generation Pendulum-A/B out-of-plane twin-satellite formation in this paper. Firstly, the Earth＇s gravity field complete up to degree and order 100 is, respectively, recovered by the collinear and pendulum satellite formations using the orbital parameters of the satellite and the matching accuracies of key payloads from the twin GRACE satellites. The research results show that the accuracy of the Earth＇s gravity field model from the Pendulum-A/B satellite formation is about two times higher than from the collinear satellite formation, and the further improvement of the determination accuracy of the Earth＇s gravity field model is feasible by the next-generation Pendulum-A/B out-of-plane twin-satellite formation. Secondly, the Earth＇s gravity field from Pendulum-A/B complete up to degree and order 100 is accurately recovered based on the orbital parameters of the satellite （e.g., an orbital altitude of 400 km, an intersatellite range of 100 km, an orbital inclination of 89° and an orbital eccentricity of 0.001）, the matching accuracies of space- borne instruments （e.g. 10-6 m in the intersatellite range, 10-3 m in the orbital position, 10-6 m/s in orbital velocity, and 10-11 m/s2 in non-conservative force）, an observation time of 30 days and a sampling interval of 10 s. The measurement accuracy of the Earth＇s gravity field from the next-generation Pendulum-A/B out-of-plane twin-satellite formation is full of promise for being improved by about l0 times compared with that from the current GRACE satellite formation. Finally, the physical requirements for the next-generation Pendulum-A/B out-of-plane twin-satellite formation are analyzed, and it is proposed that the satellite orbital altitude be preferably designed to be close to 400±50 km and the matching precision of key sensors from the Pendulum-A/B mission be about one order of magnitude higher tha     

Torsional oscillations in a nonequatorial orbit in Lenzs-Thirring metric

The authors investigate the forced oscillations of a torsional pendulum oriented in a definite way on a platform traveling in a circular nonequatorial orbit around a source of a Lenze-Thirring metric (in particular, around the earth). This general relativistic effect is associated with the inception in the platform reference frame of periodic inertial forces acting on the ends of the pendulum, with a period equal to the time of rotation of the platform in its own reference frame.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 47–50, January, 1982.     

Existence of dual mass: Experimental evidence

This second article on dual mass investigates the physical evidence for the existence of dual mass. We discuss three possible observations that could be used to bound the amount of dual mass in the solar system: the Eotvos experiment, the relativistic pendulum, and planetary orbits. The Eotvos experiment is used to conclude that the ratio of dual mass to ordinary mass is a constant. Under this assumption the dual mass effects are proportional to a dimensionless parameter which is proportional to the ratio of dual to ordinary mass. We consider two effects: First we show that a pendulum swinging in the gravitational field of the earth would be subject to a precession of the plane of oscillation; second, we show that dual mass in the solar system creates a lifting of planetary orbits. Observations of a pendulum should yield to an accuracy of 10^–4 and limits on the detectability of the planetary lifting puts an upper bound on of about 10^–1.     

Inverting chaos: Extracting system parameters from experimental data

Given a set of experimental or numerical chaotic data and a set of model differential equations with several parameters, is it possible to determine the numerical values for these parameters using a least-squares approach, and thereby to test the model against the data? We explore this question (a) with simulated data from model equations for the Rossler, Lorenz, and pendulum attractors, and (b) with experimental data produced by a physical chaotic pendulum. For the systems considered in this paper, the least-squares approach provides values of model parameters that agree well with values obtained in other ways, even in the presence of modest amounts of added noise. For experimental data, the "fitted" and experimental attractors are found to have the same correlation dimension and the same positive Lyapunov exponent. (c) 1996 American Institute of Physics.     

组合式摆动实验仪的研制

介绍一种组合式摆动实验仪,它可以将三线摆、两线摆、扭摆和单摆这四种实验仪器巧妙组合在一起,成为一种新的实验仪,具有一台实验仪测量多种摆动的功能,可以实现多种物理量的测量以及对不同摆动规律的研究,有效节约购置仪器成本。     

基于编码器的复摆设计与实验研究

针对复摆实验,设计了一种基于编码器的复摆实验装置。该装置将摆锤和多孔摆结合起来,可以采用多种方式对重力加速度、转动惯量进行求解,并验证了刚体的平行轴定理。在实验过程中,采用Matlab进行最小二乘法线性拟合,创新性地完成了对重力加速度的求解和平行轴定理的验证。实验结果表明,相比于传统的复摆,该装置更为简便,精度更高。     

用改进的单摆实验系统与Spss标定重力加速度

对传统的单摆实验系统进行改进及调试,用电磁铁控制摆球起始状态的一致性,调节光电门至摆球所处最低平衡位置的正下端,用记时记数测速仪精准测定摆球振动的周期。通过对测量原理、不确定度的分析,引入Spss的曲线估计功能分析实验数据,得出实验系统的有效摆长复合量与摆球振动周期平方的定标曲线,并验证出有效摆长复合量与摆球振动周期的平方存在线性关系,由此标定出重力加速度,并用置信概率为95%的不确定度,对测量数据及其实验结果进行合理的分析和估算,最终得出较为合理的实验结果。