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%                            Michael Pokojovy                             % 
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set(gcf, 'PaperUnits', 'centimeters');
xSize = 14; ySize = 12;
xLeft = (21 - xSize)/2; yTop = (30 - ySize)/2;
set(gcf,'PaperPosition', [xLeft yTop xSize ySize]);
set(gcf,'Position',[0 0 xSize*50 ySize*50]);

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figure(1);
hold on;
t = title('Das Vektorfeld $v(x) = \varphi(|x|) (-x_{2}, x_{1})^{T}$, $\varphi(r) = 2 + r \cos(r)$', 'interpreter', 'latex');
set(t, 'FontSize', 16);

phi = @(r) 2 + r.*cos(r);

N = 10;
M = 30;

X = zeros(N, M);
Y = zeros(N, M);

for i = 1:N
for j = 1:M
   X(i, j) = 2*i/N*cos(2*pi*(j - 1)/(M - 1));
   Y(i, j) = 2*i/N*sin(2*pi*(j - 1)/(M - 1));
end
end
 
R = sqrt(X.^2 + Y.^2);

U = -Y.*phi(R);
V =  X.*phi(R);

quiver(X, Y, U, V);

phi = linspace(0, 2*pi, 100);
plot(cos(phi), sin(phi), 'r');

xlabel('x_{1}');
ylabel('x_{2}');