Transcendental equation solution solution, graph plot.
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Hello All,
I am trying to solve transcendental equation and plot graph for left and right part of this equation (g.c(1+r)=n+(1/pi)*atan(-(A/B))). It suppose to look like the attached images constants are also mention there.
n>2 n=(3:1:8) and c>0 c=(1:0.2:2).
Where A and B are
A=cos(g.*c.*pi.*r).*cos(g.*sqrt((c.^2)-1).*pi.*r)+sqrt(1-(1./(c.^2))).*sin(g.*c.*pi.*r).*sin(g.*sqrt(c.^2-1).*pi.*r);
B=sin(g.*c.*pi.*r).*cos(g.*sqrt((c.^2)-1).*pi.*r)-sqrt(1-(1./(c.^2))).*cos(g.*c.*pi.*r).*sin(g.*sqrt(c.^2-1).*pi.*r);
I tried this on Matlab:
close all clc;
g = sqrt(8); r = 0.20;
n = 3:1:8; c = 1:0.2:2;
A_S=cos(g.*c.*pi.*r).*cos(g.*sqrt((c.^2)-1).*pi.*r)+sqrt(1-(1./(c.^2))).*sin(g.*c.*pi.*r).*sin(g.*sqrt(c.^2-1).*pi.*r); B_S=sin(g.*c.*pi.*r).*cos(g.*sqrt((c.^2)-1).*pi.*r)-sqrt(1-(1./(c.^2))).*cos(g.*c.*pi.*r).*sin(g.*sqrt(c.^2-1).*pi.*r);
A_A=cos(g.*c.*pi.*r).*sin(g.*sqrt((c.^2)-1).*pi.*r)-sqrt(1-(1./(c.^2))).*sin(g.*c.*pi.*r).*cos(g.*sqrt(c.^2-1).*pi.*r); B_A=sin(g.*c.*pi.*r).*sin(g.*sqrt((c.^2)-1).*pi.*r)+sqrt(1-(1./(c.^2))).*cos(g.*c.*pi.*r).*cos(g.*sqrt(c.^2-1).*pi.*r);
F=g*c*(1+r);
T_S=atan(-(A_S./B_S)); w_S=(n+(1/pi)).*T_S;
T_A=atan(-(A_A./B_A)); w_A=(n+(1/pi)).*T_A;
figure; plot(c,F,'b') hold on; plot(c, w_S ,'r') plot(c, w_A, 'g') grid on hold off;
Thank you!
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Answers (1)
Arun Mathamkode
on 22 Aug 2017
If your implementation of the equations are right, then this might work
close all
clc;
g = sqrt(8);
r = 0.20;
%n = 3:1:8;
c = 1:0.2:2;
A_S=cos(g.*c.*pi.*r).*cos(g.*sqrt((c.^2)-1).*pi.*r)+sqrt(1-(1./(c.^2))).*sin(g.*c.*pi.*r).*sin(g.*sqrt(c.^2-1).*pi.*r);
B_S=sin(g.*c.*pi.*r).*cos(g.*sqrt((c.^2)-1).*pi.*r)-sqrt(1-(1./(c.^2))).*cos(g.*c.*pi.*r).*sin(g.*sqrt(c.^2-1).*pi.*r);
A_A=cos(g.*c.*pi.*r).*sin(g.*sqrt((c.^2)-1).*pi.*r)-sqrt(1-(1./(c.^2))).*sin(g.*c.*pi.*r).*cos(g.*sqrt(c.^2-1).*pi.*r);
B_A=sin(g.*c.*pi.*r).*sin(g.*sqrt((c.^2)-1).*pi.*r)+sqrt(1-(1./(c.^2))).*cos(g.*c.*pi.*r).*cos(g.*sqrt(c.^2-1).*pi.*r);
F=g*c*(1+r);
plot(c,F,'b')
for n=3:8
T_S=atan(-(A_S./B_S));
w_S=(n+(1/pi)).*T_S;
T_A=atan(-(A_A./B_A));
w_A=(n+(1/pi)).*T_A;
hold on;
plot(c, w_S ,'r')
plot(c, w_A, 'g')
end
grid on
hold off;
end
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