弹跳运动的Simulink仿真模拟

本文建立了小球在谐振桌面上做弹跳运动的动力学模型,并用Simulink仿真软件模拟了小球在不同参数下从规则运动到无规则运动的各种动力学行为,仿真的结果表明,控制参数对系统的动力学行为有重要的影响.     

弹跳运动中混沌现象的电子模拟

给出了一个电子实验电路，用以模拟刚性小球在振动台面上的弹跳运动，可给出在逐渐增大台面的振动幅度或振动频率时，小球表现出的从规则运动到无规运动的各种动力学行为。     

“能量穿梭机”实验中的类星体运动

通过理论分析建立动力学方程,用四阶Runge-Kutta进行求解,研究了"能量穿梭机"实验仪中的类星体运动.不考虑阻力时,小球会进动并且进动角随圆锥面倾斜角的增大而减小,当倾斜角约为55.6°时,进动消失,小球做类似星体的椭圆运动.考虑阻力时,由于能量损失小球的运动不再有周期性,这与小球在圆锥面上的真实运动相符.     

浅谈“离心浮力”参与作用下小球的运动

流体在做匀速旋转运动时会产生与静止状态不同的动力学效应,主要体现在液体内部的压强变化以及由此带来的附加浮力,可形象地称之为"离心浮力".本文就V形管惯性离心力演示仪中的小球运动问题进行深入讨论,通过求解曲面积分求得小球所受"离心浮力"公式,进而求出小球的运动方程,并对实验中出现的现象进行定量分析解释.     

关于几个典型的刚体运动问题中被动力作用的教学讨论

在存在约束的动力学问题中,有关被动力作用的分析一直是大学物理教学中的薄弱环节,因而可能导致学生对这类问题的错误理解和求解。本文结合小球与匀质细杆碰撞问题、摩擦轮问题和旋转轮摩擦加速问题等3个典型问题讨论了大学物理教学中的被动力在刚体运动中的作用,即特别是小球与匀质悬挂杆的碰撞问题。讨论力求便于学生理解,因此推导尽量简单。文章认为,讨论有约束的刚体动力学问题时必须强调约束是通过被动力对刚体的运动带来作用。这是使学生正确理解和求解刚体动力学问题的关键之一。     

基于Matlab和VR场景的液体粘滞系数演示实验的制作与仿真

针对在＂落球法测量液体粘滞系数＂的实验中,小球在液体中开始匀速运动的时间和位置很难判定,我们使用Matlab/Simulink仿真软件的虚拟现实（VR）工具箱制作了＂落球法测量液体粘滞系数＂的演示实验,对蓖麻油中小球的运动规律进行了动态的仿真,并将仿真结果与真实的实验结果进行了比较和分析,这将有助于提高学生对实验结论的认识和理解。     

利用物理仿真实验室研究绳系小球系统在复合场中运动

利用物理仿真实验室模拟了绳系小球系统在复合场中的运动,首先分别将小球从A,C点静止释放,获取了小球的速率与加速度大小随时间的变化关系图,分析原因,总结规律,随后通过不断改变小球静止释放的位置,观察小球的运动轨迹,得出小球做部分圆周运动的条件,最后计算出小球从直线到圆周运动的临界位置以及在该位置所损失的机械能.     

竖直平面内“ 轻绳模型”的运动规律研究

利用理论研究与“ 仿真物理实验室”实验验证相结合的方法, 研究了竖直平面内的“ 轻绳模型”这一重 要的单轨道模型问题, 分析了小球速度、 加速度图像和规律, 研究得到了小球不能完成完整圆周运动的初速度条件; 小球做完整的竖直平面内圆周运动的初速度条件; 小球沿圆弧“ 轨道”返回的初速度条件; 小球离开圆弧“ 轨道”做 斜抛运动的最低点初速度条件以及斜抛运动的速度大小和方向; 阐述了小球从最低点水平方向出发经圆弧上某点 斜抛运动后能返回初始点的初速度条件; 并给出落点在最低点( 出发点)左右两侧侧圆弧上的初速度条件     

弹簧车摆的动力学模拟研究

弹簧牵引下的车摆模型是一个复杂的不可积非线性动力学体系,采用牛顿力学定律建立了车摆模型的动力学方程,运用Matlab软件进行计算机数值模拟并详细讨论了车摆模型中小球和车随时间动力学演化过程和运动特征。研究发现摆球的运动在多数情况下是混沌的,同时也会出现拟周期运动,并在一定范围内出现混沌和拟周期运动并存且交替变化的阵发性混沌运动现象。直观描绘出摆球运动中轨迹图、相图、时域图对下落角度初始值的极端敏感依赖性。通过数值模拟处理不可积系统得到的计算结果为车摆相关模型的物理教学和研究提供参考依据。     

基于Matlab GUI落球法测液体黏度的虚拟仿真设计

针对传统落球法测液体黏度实验的局限性,基于MATLAB GUI设计了虚拟仿真实验.该虚拟仿真实验直观给出小球在液体中的运动规律,提供了液体温度对黏度的影响、无限广延条件的实现、不同直径小球匀速下落的起点以及生活常见液体的黏度等实验探究模块.另外,该虚拟仿真实验还结合实体实验设计了实验预习、实验探究和实验考核等学习模块.在不同的实验模块均设置了可调节的参数,允许操作者根据需要进行相关规律的探究,并且该虚拟仿真实验能够自动分析实验结果、可视化生成实验变量关系图.     

Irregular diffusion in the bouncing ball billiard

We call a system bouncing ball billiard if it consists of a particle that is subject to a constant vertical force and bounces inelastically on a one-dimensional vibrating periodically corrugated floor. Here we choose circular scatterers that are very shallow, hence this billiard is a deterministic diffusive version of the well-known bouncing ball problem on a flat vibrating plate. Computer simulations show that the diffusion coefficient of this system is a highly irregular function of the vibration frequency exhibiting pronounced maxima whenever there are resonances between the vibration frequency and the average time of flight of a particle. In addition, there exist irregularities on finer scales that are due to higher-order dynamical correlations pointing towards a fractal structure of this curve. We analyze the diffusive dynamics by classifying the attracting sets and by working out a simple random walk approximation for diffusion, which is systematically refined by using a Green–Kubo formula.     

Randomness in the bouncing ball dynamics

The dynamics of a vibrated bouncing ball is studied numerically in the reduced impact representation, where the velocity of the bouncing ball is sampled at each impact with the plate (asynchronous sampling). Its random nature is thus fully revealed: (i) the chattering mechanism, through which the ball gets locked on the plate, is accomplished within a limited interval of the plate oscillation phase, and (ii) is well described in impact representation by a special structure of looped, nested bands and (iii) chattering trajectories and strange attractors may coexist for appropriate ranges of the parameter values. Structure and substructure of the chattering bands are well explained in terms of a simple impact map rule. These results are of potential application to the analysis of high-temperature vibrated granular gases.     

摩擦力对非弹性蹦球倍周期运动的影响

分析了摩擦力对竖直振动台面上完全非弹性蹦球动力学行为的影响.当控制参数Γ由1逐渐增大时,作用在蹦球上的恒定摩擦力不会改变倍周期分岔的序列,但会使倍周期分岔点的数值变大.与无摩擦力时的情况相比,在飞行时间的分岔图中也存在倍周期分岔密集区,只是被横向拉伸纵向压缩,且具有不同的分形特性.与受振颗粒体系中的倍周期分岔过程做了比较,发现当摩擦力取值为颗粒总重量的20%—30%时两者符合很好.     

完全非弹性蹦球的动力学行为

对振动台面上的完全非弹性球的蹦跳行为进行了初步分析.受约化振动加速度的控制，球的运动可以表现出一系列倍周期分岔过程.对几种典型的倍周期运动及分岔情况进行了讨论. 关键词： 蹦球 倍周期分岔 混沌 颗粒物质     

Subharmonic bifurcations and chaotic dynamics of an air damping completely inelastic bouncing ball

We investigate the dynamics of a plastic ball on a vibrated platform in air by introducing air damping effect into the completely inelastic bouncing ball model. The air damping gives rise to larger saddle-node bifurcation points and a chaos confirmed by the largest Lyapunov exponent of a one-dimensional discrete mapping. The calculated bifurcation point distribution shows that the periodic motion of the ball is suppressed and a chaos emerges earlier for an increasing air damping. When the reset mechanism and the linear stability which cause periodic motion of the ball both collapse, the investigated system is fully chaotic.     

On the quantum Fermi accelerator and its relevance to ‘quantum chaos’

We discuss a quantum version of the Fermi acceleration model, which consists of a particle bouncing between a fixed and oscillating wall. The actual movement of the particle crucially depends on the boundary conditions of the Schrödinger equation. Under Dirichlet boundary conditions, the quantum system displays a regular behaviour, but its classical limit exhibits some unphysical attributes. Only for certain initial conditions does it correspond to the stable motion of a ball bouncing once for an integer number of wall oscillations. In the classical model that situation gives rise to regular islands imbedded in the chaotic sea.     

Control of implicit chaotic maps using nonlinear approximations

The technique of using nonlinear approximations to design controllers for chaotic dynamical systems introduced by Yagasaki and Uozumi is extended in order to enable it to be used to design controllers for chaotic dynamical systems that are described by implicit maps and is then used to control the well-known bouncing ball system without recourse to the high-bounce approximation. (c) 2000 American Institute of Physics.     

Acceleration noise generated by a random repeated impact process

Acceleration noise levels generated by a random repeated impact process have been predicted and compared with experimental measurements. The process consisted of a ball bouncing on a randomly vibrating surface, and is an idealized representation of random impact phenomena which can occur in machinery and transportation systems where a rolling element is in intermittent contact with the rolling surface. Predictions of the magnitudes of impacts and the times between them have been used in conjunction with established acoustic theory to estimate acceleration noise levels generated by the impacting ball. Measured sound pressure levels were in excellent agreement with the predicted levels.