I want to get a scaled vector field $\vec F=(x^2-x)i+(y^2-y)j$. The Fig should be like the attached Fig:

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Atom
Atom 2023-12-25
回答： Sulaymon Eshkabilov 2023-12-25
I want to get a scaled vector field $\vec F=(x^2-x)i+(y^2-y)j$. The Fig should be like the attached Fig:
[x,y] = meshgrid(-2:.16:2,-2:.16:2);
Fx = (x.*x-x);
Fy=y.*y-y;
figure;
quiver(x,y,Fx,Fy,'k','linewidth',1.2)
hold on
x=-2:0.01:2;
y=1-x;
plot(x,y,'k','linewidth',2);
Note that we have $div \vec F>0$ for $x+y>1$, $div \vec F<0$ for $x+y<1$ and $div \vec F=0$ on the line $x+y=1$ .
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Dyuman Joshi
Dyuman Joshi 2023-12-25
What is the vector field scaled to?
The arrows of the vector field in the reference image appear to be of the same length.

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Sulaymon Eshkabilov
Sulaymon Eshkabilov 2023-12-25
Ran in:
Is this what you are trying to obtain:
[x, y] = meshgrid(-2:0.25:2); % x and y values
F_x = 1*(x.^2 - x); % The vector field of x
F_y = 1*(y.^2 - y); % The vector field of y
F = F_x+F_y;
% Normalize the vectors
magnitude = sqrt(F_x.^2 + F_y.^2);
F_x_Nor = F_x ./ magnitude;
F_y_Nor = F_y ./ magnitude;
% Plot the scaled vector field
quiver(x, y, F_x_Nor, F_y_Nor);
hold on
X=-2:0.1:2;
Y=1-X;
plot(X,Y,'k','linewidth',2);
xlabel('x');
ylabel('y');
title('Scaled Vector Field: F = (x^2 - x) + (y^2 - y)');
axis([-2 2 -2 2])

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