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Freemat Exponential Screw Recipe

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Plotting the Exponential S

t = linspace(0, 3*pi, 1000);
f = exp(i*t);
sizefig(640,800)
plot3(real(f), imag(f), t, 'LineWidth',3)
hold on
plot3(cos(t),zeros(size(t))-3, t);
plot3(zeros(size(t))-3, sin(t), t);
plot3(cos(t), sin(t), zeros(size(t)));
grid on
axis([-3 3 -3 3 0 4*pi] )
view(125,65)
zlabel('T')
xlabel('I')
ylabel('R')
title('Euler''s Formula')

 x = 0:0.1:10;
 yz = exp(1i*x);
 plot3(x, real(yz), imag(yz))
 ylabel('\Re(e^{1i*x})');
 zlabel('\Im(e^{1i*x})');
t = linspace(0, 3*pi, 500);
f = exp(i*t);
figure
plot3(real(f), imag(f), t, 'LineWidth',3)
hold on
plot3(real(f), zeros(size(t))+1.5, t)
plot3(zeros(size(t))-2, imag(f), t)
grid on
axis([-2 2 -1.5  1.5 0 3*pi] )
view([-125  30])
t = linspace(0, 2.5, 250);
f = exp(2*pi*4/2.5*1i*t);

figure(1)
plot3(t, real(f), imag(f), 'LineWidth',2)
hold on
plot3(t, real(f), zeros(size(t))-1.5)
plot3(t, zeros(size(t))-2, imag(f))
hold off
grid on
axis([-1  3    -2  2    -1.5  1.5])
view([-125  30])
xlabel('Time', 'Rotation',-30)
ylabel('Real Axis', 'Rotation',10)
zlabel('Imag Axis')

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Categories: Freemat

Tags: Xxx Exponential Xxx Euler


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This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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