Plotting a vector field in an annulus
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Here is the problem:
Suppose I have an annulus with inner radius 0.71392 and the outer radius 1. I want to plot a vector field on the annulus, where the vectors are unit tangent vectors to the concentric circles within the annulus. Here is the geometry I am talking about:
t=0:0.001:2*pi;
x=cos(t);
y=sin(t);
x1=0.71392*cos(t);
y1=0.71392*sin(t);
x2=cos(t);
y2=sin(t);
plot(x,y,'r',x1,y1,'b',x2,y2,'g');
axis equal
Any suggestion would be greatly appreciated.
采纳的回答
clc; clear all ;
t=0:0.001:2*pi;
x=cos(t);
y=sin(t);
x1=0.71392*cos(t);
y1=0.71392*sin(t);
x2=cos(t);
y2=sin(t);
% Unit tangent vectros
dx1 = gradient(x1) ;
dy1 = gradient(y1) ;
modv1 = sqrt(dx1.^2+dy1.^2) ;
Tx1 = dx1./modv1 ;
Ty1 = dy1./modv1 ;
dx2 = gradient(x2) ;
dy2 = gradient(y2) ;
modv2 = sqrt(dx2.^2+dy2.^2) ;
Tx2 = dx2./modv2 ;
Ty2 = dy2./modv2 ;
plot(x1,y1,'b',x2,y2,'g');
axis equal
hold on
idx = 1:200:length(x1) ;
quiver(x1(idx),y1(idx),Tx1(idx),Ty1(idx),'r')
quiver(x2(idx),y2(idx),Tx2(idx),Ty2(idx),'r')
5 个评论
Avishek Mukherjee
2021-8-9
@KSSV, Thanks for the suggestion.
I think the above code creates vector field of unit tangent vectors on the inner and the outer circle. When executed, it gives me the following figure:
What I want is a quiver plot of vector field inside the annulus such that the vector field inside the annulus consists of unit vectors that are tangent to the concentric circles inside the annulus, for example, something like this:
KSSV
2021-8-9
Check the figure.....
Avishek Mukherjee
2021-8-9
KSSV
2021-8-9
Generate the radii, make circel and follow the same.,
Avishek Mukherjee
2021-8-9
@KSSV, I can do it manually. But instead of manually doing it, I created a sequence of radii and created a vector field for each of the radii inside the annulus. The code I implented is this:
t=0:0.001:2*pi;
r = 0.71392:4.5526e-05:1;
x=cos(t);
y=sin(t);
x1=r.*cos(t);
y1=r.*sin(t);
x2=cos(t);
y2=sin(t);
% Unit tangent vectros
dx1 = gradient(x1) ;
dy1 = gradient(y1) ;
modv1 = sqrt(dx1.^2+dy1.^2) ;
Tx1 = dx1./modv1 ;
Ty1 = dy1./modv1 ;
dx2 = gradient(x2) ;
dy2 = gradient(y2) ;
modv2 = sqrt(dx2.^2+dy2.^2) ;
Tx2 = dx2./modv2 ;
Ty2 = dy2./modv2 ;
plot(x1,y1,'b',x2,y2,'g');
axis equal
hold on
idx = 1:200:length(x1) ;
quiver(x1(idx),y1(idx),Tx1(idx),Ty1(idx),'r')
quiver(x2(idx),y2(idx),Tx2(idx),Ty2(idx),'r')
which produces a spiral:
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