MATLAB: Solve IVP with ode45

MATLABode45

So I am trying to generate an ODE45 graph with the file provided. I made the modification which I believe are correct but the graph generated at the output is not correct. The second function
function dYdt=f(x,Y)
has a modified version of my function and I am wondering if that is causing the ODE function not to generate the proper input. Would anyone be able to advise on a solution or where I am going wrong ?
Thank you

Best Answer

Looks like your equation is not correct for non-linear pendulum! Try the following:
% If u = angle from vertical then  d^2u/dt^2 = -(g/l)sin(u)
%
%   Let v = du/dt;  dv/dt = -(g/l)sin(u);
Y0 = [1 2];
tspan = 0:0.1:10;
ge = 32; % Earth
[t, Y] = ode45(@f, tspan, Y0, [], ge);
ue = Y(:,1);
gm = 0.165*ge;
[t, Y] = ode45(@f, tspan, Y0, [], gm);
um = Y(:,1);
plot(t, ue, t, um), grid
xlabel('time'), ylabel('angle')
legend('Earth','Moon')
function dYdt = f(~,Y,g)
        
        l = 3;
        u = Y(1);
        v = Y(2);
        dudt = v;
        dvdt = -g/l *sin(u);
        dYdt = [dudt; dvdt];
end
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