I am trying to determine the coefficient q in the parametrization of a epicycloid which gives me the arc length of 4.25. The parametrization can be glimpsed in my attempt of a solution in the following Matlab code.
t = 0:0.01:2*pi;
fun = @(t,q) sqrt((c.^2).*(r.^2).sin(t).^2+(c.^2).(q.^2).*(r.^2).*sin(c.t).^2+(c.^2).(r.^2).cos(t).^2+(c.^2).(q.^2).*(r.^2).*cos(c.*t).^2+1);
fun2 = @(q) integral(@(t) fun(t,q),0,2*pi)
qsolve=fsolve(@(q) fun2(q)-4.25, 0)
The problem is that solve can not find any solution. I am very much grateful if someone can help me with this one.