Transcendental equation solution solution, graph plot.

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!

Answer 1

[Arun Mathamkode]

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