MATLAB模拟伽尔顿板实验

MATLAB模拟伽尔顿板实验代码展示：

clear;b=1;k=1;dxdy=0.81;r=0.1;ttt=0:pi/300:2*pi;xxx=r*exp(i*ttt);for n=1:80for m=10:20if xor(mod(m,2),mod(n,2))xy0(1,k)=dxdy*n;xy0(2,k)=dxdy*m;ax=xy0(1,k);ay=xy0(2,k);plot(xxx+-1+i*(-2),'r.'), plot(ax,ay,'r.','markersize',15) ,hold onk=k+1;endendendk0=k-1;axis ([-3 n*dxdy+3 -2 m*dxdy+5])ll=40/80*dxdy;L=3000;r1=n/2*dxdy*ones(1,L)+[1.5*dxdy*rand(1,L/2) -1.5*dxdy*rand(1,L/2)];r2=(m*dxdy+1)+1.5*dxdy*rand(1,L);xyxy=[r1;r2];xy=[r1;r2];vy=-1*rand(1,L);vx=[2*rand(1,L/2) -2*rand(1,L/2)];v=[vx;vy];ball=plot(r1(1,:),r2(1,:),'.','markersize',15,'color','b')hold offpausexy=xyxy;m=1;for k=1:3000dt=0.015;g=59.8;vxm(k)=mean(v(1,:));vym(k)=mean(v(2,:));vxstd(k)=std(v(1,:));vystd(k)=std(v(2,:));for numball=1:Lif xy(2,numball)<=5xy(2,numball)=5;v(2,numball)=0;v(1,numball)=0;endif xy(1,numball)<dxdy | xy(1,numball)>=n*dxdyxy(1,numball)=(xy(1,numball)<dxdy)*(2*dxdy-xy(1,numball))+(xy(1,numball))>n*dxdy)*(2*n*dxdy-xy(1,numball));v(1,numball)=-v(1,numball);enddtt=dt/3*2;dttt=dt/3;dtttt=dt/2;xy(1,numball)=xy(1,numball)+dt*v(1,numball);xy(2,numball)=xy(2,numball)+dt*v(2,numball)-0.5*g*dt^2;v(2,numball)=v(2,numball)-g*dt;if xy(2,numball)>10*dxdy  al=xy(1,numball)-dtt*v(1,numball);all=xy(1,numball)-dttt*v(1,numball);alll=xy(1,numball)-dtttt*v(1,numball);bl=xy(2,numball)-dtt*v(2,numball)-0.5*g*dtt^2;bll=xy(2,numball)-dttt*v(2,numball)-0.5*g*dttt^2;blll=xy(2,numball)-dtttt*v(2,numball)-0.5*g*dtttt^2;cl=[al;bl];cll=[all;bll];clll=[alll;blll];for numxy=1:k0dxy=norm(xy(:,numball)-xy0(:,numxy));dxyl=norm(cl-xy0(:,numxy));dxyll=norm(cll-xy0(:,numxy));dxylll=norm(clll-xy0(:,numxy));if dxy<=0.38 | dxyl<=0.38 | dxyll<=0.38 | dxylll<=0.38xy(:,numball)=xyxy(:,numball);v(2,numball)=v(2,numball)+g*dt;    a=xy(1,numball);b=v(1,numball);c=xy(2,numball);d=v(2,numball);e=xy0(1,numxy);f=xy0(2,numxy);t = fsolve(@myfun2,0.000,optimset('Display','off'),a,b,c,d,e,f,g);t0=min(t);xy(1,numball)=xy(1,numball)+t0*v(1,numball);xy(2,numball)=xy(2,numball)+t0*v(2,numball)-0.5*g*t0^2;%set(ball,'xdata',xy(1,:),'ydata',xy(2,:));v(2,numball)=v(2,numball)+g*t0;y1=xy(2,numball);y2=xy0(2,numxy);x1=xy(1,numball);x2=xy0(1,numxy);vx=v(1,numball);vy=v(2,numball);axy=atan((y2-y1)/(x2-x1+eps));v(1,numball)=(-vx*cos(2*axy)-vy*sin(2*axy));v(2,numball)=(vy*cos(2*axy)-vx*sin(2*axy));t0=dt-t0;xy(1,numball)=xy(1,numball)+t0*v(1,numball);xy(2,numball)=xy(2,numball)+t0*v(2,numball)-0.5*g*t0^2;v(2,numball)=v(2,numball)-g*t0;endend endendxyxy=xy;set(ball,'xdata',xy(1,:),'ydata',xy(2,:));drawnow;endfigure(1)histfit(xy(1,:),31)figure(2); m=1:k;kk=m*dt;plot(kk,vxm,'r:',kk,vym,'b-')figure(3); plot(kk,vxstd,'r:',kk,vystd,'b-')figure(4)vx1=diff(vxm);vy1=diff(vym);n=1:(k-1);kkt=n*dt;plot(kkt,vx1,'r:',kkt,vy1,'b-')

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MATLAB模拟伽尔顿板实验

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