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。     

Occurrence of stable periodic modes in a pendulum with cubic damping

Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the harmonic balancing method; the resulting nonlinear response curves are studied further for resonance and stability of symmetric oscillations with relatively low damping. The stability analysis is carried out by transforming the system of equations to the linear Mathieu equation.     

简易旋转倒立摆及控制装置的系统设计简

采用ATmega128作为本旋转倒立摆控制装置的主控芯片,通过直流电机对旋转臂进行控制,实现对摆杆的旋转控制。用编码器对摆杆旋转角度进行测量,将旋转位移转换成数字脉冲实现控制。通过对编码器设定零点,运用PID算法实现精确控制摆杆的摆动角度与状态。测试结果表明,该简易旋转倒立摆及控制装置的系统设计方法科学,具有性能稳定、抗干扰能力强、控制精确,可靠性高,节能环保等优点。     

Tunneling of trapped-atom Bose condensates

We obtain the dynamics in number and phase difference, for Bose condensates that tunnel between two wells of a double-well atomic trap, using the (nonlinear) Gross-Pitaevskii equation. The dynamical equations are of the canonical form for the two conjugate variables, and the Hamiltonian corresponds to that of a momentum-shortened pendulum, supporting a richer set of tunneling oscillation modes than for a superconductor Josephson junction, that has a fixed-length pendulum as a mechanical model. Novel modes include ‘inverted pendulum’ oscillations with an average angle of π; and oscillations about a self-maintained population imbalance that we term ‘macroscopic quantum self-trapping’. Other systems with this phase-number nonlinear dynamics include two-component (interconverting) condensates in a single harmonic trap, and He³B superfluids in two containers connected by micropores.     

弹簧摆在匀强磁场中的运动分析

针对带有电荷的弹簧摆施加在竖直方向的匀强磁场的背景下,通过牛顿力学的方法得到了其运动学方程,从而发现其摆动平面在不停的进行旋转.同时按照初始条件的不同,将其在水平方向上的运动学方程化简为不同的曲线方程,进而得到了其运动的轨迹特征.     

傅科摆模拟演示装置的研制

介绍一种傅科摆模拟演示装置．该装置具有体积小、操作方便、演示效果显著、演示时间短、摆振动平面的偏转周期可人为控制以及对摆锤的运动轨迹可作永久记录等优点．     

“舍割”摆中共轭点的妙用

文章介绍了利用共轭点可以测量等值摆长、重力加速度、周期和转动惯量等。     

激光单摆演示仪的研制与应用

设计的激光单摆演示仪是利用霍尔传感器测量摆球的摆动周期,通过演示仪底盘上的小型激光器可观测摆动面的偏转,将计时、计数、测角等功能合为一体,有效摆动时间内能够分辨出地球的自转现象.     

E-measure混沌摆的数学解析与运动方程

首先阐述了混沌摆的科学描述;其次对混沌摆进行了数学解析,分析了瞬衰解和稳态解的作用;然后构建了混沌摆的运动方程。得到了E-measure混沌摆实验必须满足的两个前提条件;加深了对混沌现象的深入了解。     

三线摆周期的旋转矢量求法

由能量方程出发，引入新变量，用旋转矢量法讨论了三线摆大角度摆动时的周期。     

转子耦合摆系统的同步行为理论研究

转子耦合摆系统广泛应用于航空动力装置、矿业筛分机械和并联机器人等高速旋转设备.但是对转子耦合摆系统同步行为(稳定相位差值)研究甚少,系统同步行为通常影响系统的工作执行精度.基于这一特殊背景,提出了转子与摆耦合系统的简化物理模型.利用庞加莱法研究转子耦合摆系统的同步问题,进一步揭示了该类系统同步现象的本质机理.首先运用拉格朗日方程建立了转子同向和反向旋转的系统动力方程,随后将系统动力方程转换为无量纲方程.然后利用拉普拉斯法对无量纲方程解耦,计算出了系统各个自由度的近似稳态响应解.继而采用庞加莱法导出了系统实现同步的平衡方程和稳定准则.只有系统的物理参数同时满足系统同步平衡方程和稳定准则时,系统才能实现稳定的同步行为.通过理论研究发现,系统的同步行为主要受弹簧刚度、摆杆安装倾角和转子旋转方向的影响.同时系统同步"临界点"会造成相位差角无解,导致系统动态特性表现为混沌.最后,使用计算机模拟验证了理论计算的正确性,两者的结果相符.     

Measurement and analysis of complex modulated motions in a weakly nonlinear system

The two-timing dynamics of a forced, weakly nonlinear system are considered. Experimental results on a roll-forced spherical pendulum verify the occurrence of slow-time, subharmonically and chaotically modulated oscillations in a frequency band near resonance; the modulatory behavior follows the occurrence of a Hopf bifurcation in the slow-time coordinates. A phase-sensitive detection method for experimentally isolating the slow-time behavior is described. A Lagrangian model for the pendulum is developed, and slow-time equations are presented. A two-thirds power scalling law relating roll angle to the appearance of the modulations is derived from the slow-time equations and tested with experimental results.     

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.     

Determination of the thermal noise limit in test of weak equivalence principle with a rotating torsion pendulum

Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.     

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。     

外力驱动的混沌摆实验仪在研究混沌效用上的应用

依据非线性动力学混沌理论,采用受外力驱动的转动马达装置,依托PASCO系统的数据采集软件,开发了适应大学物理实验的受外力驱动的混沌摆实验。探讨了新型基于外力驱动的混沌摆实验仪在研究混沌效用上的应用,实验发现利用该装置可以直观的研究系统的初值敏感性,奇异子现象等,操作简单、直观、灵敏度高,实验除了具有实际应用价值外,同时适合在高等学校大学物理基础实验中开设出相应的实验教学内容。     

A rotating three component perfect fluid source and its junction with empty space-time

The Kerr solution for empty space-time is presented in an ellipsoidally symmetric coordinate system and it is used to produce generalised ellipsoidal metrics appropriate for the generation of rotating interior solutions of Einstein’s equations. It is shown that these solutions are the familiar static perfect fluid cases commonly derived in curvature coordinates but now endowed with rotation. These are also shown to be potential fluid sources for not only Kerr but also Kerr-de Sitter empty space-time. The approach is further discussed in the context of T-solutions of Einstein’s equations and the vacuum T-solution outside a rotating source is presented. The interior source for these solutions is shown not to be a perfect fluid but rather an anisotropic three component perfect fluid for which the energy momentum tensor is derived. The Schwarzschild interior solution is given as an example of the approach.     

单摆系统的振动研究

通过求解变张力弦振动微分方程的边值问题,给出摆线与摆球的质量比为任意值时单摆系统运动的一般解和本征频率满足的方程.利用该方程求得高精度的单摆系统周期数值解,特别是拟合出单摆系统作基频振动时一个范围大、精度高的周期近似公式.同时将理论与实验进行比较,结果二者相符.