Plotting a non-linear graph in Matlab

Hi guys,

I have this equation f(g)=1+cos(g)*cosh(g)-a*g*(cos(g)*sinh(g)-sin(g)*cosh(g))=0. I am trying to plot it for (a,g).

I have the initial condition that when a=0 then g=1.8751.

I am not sure how to code it as an equation with two unknowns and two initial values ??

My suggestion would be to plot the graph by using the solve function by using a=a+da (where da is small increment of a) and using the previous value of g as an initial value to find g for the new value of a.

Regards, Rihab

[Muhammad Usman Saleem]

f(g)=1+cos(g)*cosh(g)-a*g*(cos(g)*sinh(g)-sin(g)*cosh(g))=0.

there are two equality sign in this equation write correct one plz

[Rihab el-Wali]

@Muhammad Usman Saleem I did mean to put two equal signs because the function is equal to zero. I want to plot (a,g) when f(g)=0.

[Muhammad Usman Saleem]

good night, tomorrow will guide u in this regards

Answer 1

[Walter Roberson]

a = linspace(-4, 2);   %the interesting part of the graph
g = zeros(size(a));

oldguess = 1.8751;
for K = 1 : length(a)
  fa = @(g) 1+cos(g)*cosh(g)-a(K)*g*(cos(g)*sinh(g)-sin(g)*cosh(g));
  this_g = fzero(fa, oldguess);
  g(K) = this_g;
  oldguess = this_g;
end

plot(a, g)

However, there are many solutions. You will, for example, get a different plot if you start with oldguess = 50

[Rihab el-Wali]

That works! However, what if I want to plot for a larger range of a? When I change the vector size from [-4,2] to [0,100] the plot seems to look different.

Answer 2

[Star Strider]

When in doubt, plot first:

[A,G] = meshgrid(-0.5:0.01:0.5, -20:0.1:20);
fga = @(a,g) 1+cos(g).*cosh(g)-a.*g.*(cos(g).*sinh(g)-sin(g).*cosh(g))
F = fga(A,G);

figure(1)
meshc(A, G, F)
grid on

There appear to be a possibly infinite number of solutions. Which one do you want?