
物理情境的模拟——欧拉法(上)
[b]1.引言[/b][br] 现代数学和物理学始于17世纪,当时艾萨克·牛顿发现了万有引力定律和运动定律,并推导出支配物体运动的微分方程.从那时起,微积分就在很多学科中都扮演着非常重要的角色.然而,大多数微分方程都是很难或不可能解的,可大学生的第一门微分方程课程通常都是在他们的大一或大二,这给学生们的学习带来了困难.然而,计算机虽不一定能给出方程的解析解,但它计算微分方程的近似解则往往较为容易.其中一种用计算机进行近似计算的基本方法被称为欧拉法.欧拉法简单、直观、清晰,而且容易学习.它甚至可以在短时间内教授给以前从没有接触过微积分的高中理科学生.[sup][[/sup][sup]1][/sup]
[b]2.欧拉法的理论背景[br][/b] 有限差分方法是一种数值解法,它的基本思想是先把问题的定义域进行网格剖分,然后在网格点上,按适当的数值微分公式将差商代替问题中的微商,从而把原问题离散化为差分形式,进而求出数值解.[sup][[/sup][sup]2][/sup][br] 将有限差分法运用于常微分方程中即为欧拉法,欧拉法用一个代数表达式代替微分方程中的导数,例如:[math]\frac{df}{dx}\approx\frac{f\left(x+\Delta x\right)-f\left(x\right)}{\Delta x}[/math]. [br] 这样替换后便可以将得到的代数方程只用算术运算来计算原常微分方程的解.[sup][3][br][/sup] 下面以常微分方程的初值问题为例,其一般形式是
(1)

所谓数值解法,就是求问题(1)的解y(x)在若干点

[br]处的近似值的方法,[math]y_n\left(n=1,2,...,N\right)[/math]称为问题(1)的数值解,[math]h_n=x_{n+1}-x_n[/math]称为[math]x_n[/math]到[math]x_{n+1}[/math]的步长。今后如无特别说明,我们总取步长为常量[math]h[/math].
建立数值解法,首先要将微分方程离散化,主要有三种方法:(1)用差商近似导数;(2)用数值积分方法;(3)用Taylor多项式近似.[br] 本节我们讨论方法(1)用差商近似导数。[br] 若采用向前差商[math]\frac{y\left(x_{n+1}\right)-y\left(x_n\right)}{h}[/math]代替[math]y'\left(x_n\right)[/math]代入(1)中的微分方程,可以得到[br] [math]\frac{y\left(x_{n+1}\right)-y\left(x_n\right)}{h}\approx f\left(x_n,y\left(x_n\right)\right)\left(n=0,1,...\right)[/math][br] 化简得[br] [math]y\left(x_{n+1}\right)\approx y\left(x_n\right)+hf\left(x_n,y\left(x_n\right)\right)[/math][br] 如果用[math]y\left(x_n\right)[/math]的近似值[math]y_n[/math]代入上式右端,所得结果作为[math]y\left(x_{n+1}\right)[/math]的近似值,记为[math]y_{n+1}[/math],则有[br] [math]y_{n+1}\approx y_n+hf\left(x_n,y_n\right)\left(n=0,1,...\right)[/math] (2)[br] 这样,问题(1)的近似解可通过求解下述问题
(2)

得到,按式(2)由初值[math]y_0[/math]可逐次计算出[math]y_1,y_2,...[/math].式(3)是个离散化问题,称为差分方程初值问题。
欧拉法就是用差分方程的初值问题的解来近似微分方程初值问题式(1)的解,即由(2)依次算出[br][math]y\left(x_n\right)[/math]的近似值[math]y_n\left(n=1,2,...\right)[/math].[sup][4][/sup][br] 为了更好地理解这样的过程,我们来看下面这个动态交互界面。
欧拉法对物理系统的分析主要分为有四个部分:陈述物理定律、推导物理过程模型、采用欧拉法将模型转化为计算方程、转化为MATLAB等计算机软件代码(后面我们会对比经典的MATLAB模拟和GeoGebra模拟,我们从中可以看到GeoGebra数值模拟的简单易行).最后运行即可给出仿真结果.[sup][1][/sup][br] 下面通过一些例子来介绍欧拉法的具体运用.[br][br][br]
[b]3.用欧拉法模拟平抛运动[/b][br][br][br]由牛顿第二定律,可得平抛运动的微分方程[br]

接着采用欧拉法将其转化为方便计算的方程,这里用到化微商为差商的思想.把微商[math]v_x=\frac{dx}{dt}[/math]化为差商有[math]v_x\left(i\right)=\frac{x\left(i+1\right)-x\left(i\right)}{\Delta t}[/math],同理可得[math]v_y\left(i\right)=\frac{y\left(i+1\right)-y\left(i\right)}{\Delta t}[/math],[math]a_y=\frac{v_y\left(i+1\right)-v_y\left(i\right)}{\Delta t}[/math],[br][br]它们在[math]\Delta t\longrightarrow0[/math]时差商变成微商,这样便可以让计算机取较小的[math]\Delta t[/math]得到结果的近似值.[br][br]再将其转化为MATLAB等计算机软件代码, MATLAB代码如下.[br]
1. m = 1; % 物体质量(单位kg) [br]2. g=10; %重力加速度大小 (单位kg/m3)[br]3. a = -g; [br]4. N = 10; % 小区间数目 [br]5. dt = 1; % 时间小区间长度 [br]6. y(1) = 0; % 初始纵坐标位置 [br]7. vx(1)=1; %初水平速度[br]8. vy(1) =0; % 初竖直速度 [br]9. t(1) = 0; % 开始时间 [br]10. x(1)=0; %初始横坐标位置 [br]11. for i = 1:N % 为实现欧拉法而作的for循环 [br]12. t(i+1) = t(i) + dt; [br]13. y(i+1) = y(i) + vy(i)*dt; % 由竖直方向上vy=dy/dt而来 [br]14. vy(i+1) = vy(i) + a*dt; % 由竖直方向上a=dvy/dt而来 [br]15. x(i+1)=x(i)+vx(i)*dt; % 由水平方向上vx=dx/dt而来 [br]16. vx(i+1)=vx(i); % 由水平方向上速度不变而来 [br]17. end [br]18. plot(x, y) % 作出x-y函数图像 [br]19. xlabel('x') [br]20. ylabel('y ')
其中[math]N[/math]和dt可决定计算的时间段。如N=100、dt=0.1时则N*dt=10s,会显示出10s内的图像。dt即为差商中的[math]\Delta t[/math],决定了计算的精确度。如图1、2所示,它们分别是N=10、dt=1时和N=100、dt=0.1时的y-x曲线。它们模拟的都是10s内初速度为[math]1\text{m/s}[/math]的平抛运动。由于dt越小则差商越近似于微商,因此我们可以看到dt越小近似效果越好。

下面我们再来看看在GeoGebra中是如何做数值模拟的。[br]下面首先是一个常规的平抛运动做法,直接写出平抛运动的水平和竖直分量的表达式,用表达式控制点的运动,让t从0开始变化,即可得到平抛运动的动态模拟。这种做法非常常规,也是大多数简单情形下,已知解析式的时候的做法。
从代数区的C点设置上就可以看出这种做平抛运动的关键思路:
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[/img]
下面的则用到了GeoGebra数值模拟技术。
当dt=0.1时
当dt=0.3时
dt=0.5时
从代数区以及一些脚本设置上可以看出GeoGebra数值模拟的关键思路。
[img]data:image/png;base64,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[/img]
t的脚本设置
赋值[p,p+dp][br]赋值[v,v+dv]
该脚本意思是无论向量p在哪里,每次t变化后都会把v+dv赋值给v,把p+dp赋值给p.[sup][5][/sup]
启动动画按钮的脚本设置
启动动画[t,true][br]赋值[p,(0,0)][br]赋值[v,(v_0,0)][br]赋值[t,0]
[b]4.用欧拉法模拟天体运动[br][/b]
已知万有引力常数[math]G\approx6.7\cdot10^{-11}[/math]m^3 / (kg·s^2),地球半径[math]R\approx6.4\cdot10^6\text{m}[/math],质量[math]M\approx6\cdot10^{24}\text{kg}[/math],同步卫星轨道距地面高度约为3600km.由[math]G\frac{Mm}{r^2}=m\frac{v^2}{r}[/math]得[math]v=\sqrt{\frac{GM}{r}}[/math].代入数值可得同步卫星做匀速圆周运动的线速度约为3.1km/s,若运行24小时,理论上轨迹应该是一个完整的圆。[br][br][br] 由牛顿第二定律和几何关系,建立微分方程有:[br][br][br]

再将微分方程和初始条件转化为计算机代码,以上6个方程分别是下面代码13-18行的理论依据.用MATLAB编程如下:(作地球图的代码省略)
[sup][/sup]1. G=6.7e-11; % 引力常数 [br]2. mEarth = 6e24; % 地球质量 [br]3. REarth = 6.4e6; % 地球半径 [br]4. dt = 0.25; % 每段小时间区间 [br]5. n = 1440*60/dt; % n*dt即为运行时间24小时 [br]6. t(1) = 0; % 开始时间 [br]7. x(1) = 0; % 同步轨道卫星位置x分量 [br]8. y(1) = REarth + 3.6e7; % 同步轨道卫星位置y分量 [br]9. vx(1) = 3.1e3; % 同步轨道卫星x方向初速度 [br]10. vy(1) = 0; % y 方向的初速度 [br]11. for i=1:n [br]12. t(i+1) = t(i) + dt; [br]13. x(i+1) = x(i) + vx(i)*dt; [br]14. y(i+1) = y(i) + vy(i)*dt; [br]15. r = sqrt(x(i)^2+y(i)^2); [br]16. a = G*mEarth/r^2; [br]17. vx(i+1)= vx(i) - a*(x(i))/r*dt; [br]18. vy(i+1)= vy(i) - a*(y(i))/r*dt; [br]19. end [br]20. plot(x,y) [sup][/sup][sup][/sup]
如图3所示,其中蓝线为同步卫星的运动轨迹,红线为地球图.理论和数值模拟结果吻合度较好,该卫星运动24小时后轨迹几乎正好是一个完整的圆.[br][br][br]
[img]data:image/png;base64,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[/img]
[br]接着通过改变初速度参数和运行时间还可以很方便的验证变轨运动的速度条件.[br][br]
理论上,若[br][img]data:image/png;base64,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[/img][br]卫星会做椭圆运动。且速度越大,椭圆越扁。若[br][img]data:image/png;base64,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[/img][br],则卫星以双曲线轨迹脱离地球吸引.即在同步卫星轨道的位置时,大概卫星速度在3.1km/s~4.3km/s时会做椭圆运动。而在大于4.3km/s时,卫星以双曲线轨迹脱离地球吸引.[sup][/sup][br] 将代码中v改为3.5km/s和4.2km/s,n改为50000*60/dt时得到如图4、5所示的两个椭圆,而将v改为4.4km/s时则可得到如图6所示的双曲线轨迹,由此可见理论和数值模拟仍符合的较好.

[b]5.用欧拉法模拟弹簧摆运动[/b]




好玩的数值模拟 欧拉法(下)
衡中弹簧摆模拟
GeoGebra不仅能做二维的模拟,还可以做三维的,因此接着我们可以更进一步,作出三维的弹簧摆模拟。

这种模拟包含了二维的弹簧摆情境,悬挂点在(0,0,0)位置,设置小球初始位置在(10,10,0),初速度为(0,0,0),g=10,k=10,m=1,L0=20时小球轨迹图如图所示.[br][br][br]

悬挂点在(0,0,0)位置,小球初始位置在(20,0),初速度为(0,1,0),g=10,k=1,m=1时小球轨迹图如图所示.

[b]6. 用欧拉法模拟带电粒子在电场中的运动[/b]
https://www.bilibili.com/video/BV1s7411F7gy?share_source=copy_web[br]我在b站中的该视频教程一步步进行了操作,并对相关脚本原理进行了解读。只要这个搞懂了,那么其他的都是类似的,都会很容易。
我的视频教程中所作的例子
在此基础上的升级版
进一步的,我们还可以做三维空间上的带电粒子在电场中的偏转,其中一个非常经典的例子就是示波器。




3D示波器原理演示
[b]参考文献[/b][br][1] Flannery W. The Coming Revolution in Physics Education[J].[br]The Physics Teacher, 2019, 57(7): 493-497.[br][2]https://baike.baidu.com/item/%E6%9C%89%E9%99%90%E5%B7%AE%E5%88%86%E6%B3%95/2949468?fr=aladdin[br][3][url=http://berkeleyscience.com/MMCCI.htm]http://berkeleyscience.com/MMCCI.htm[/url][br][br][br]