Error in using ode45 to solve a second-order ODE

I am trying to solve a fairly simple second-order ODE using the ode45 command. I've read the documentation and created a file containing the function to be solved, having reduced it to state space form. The file is called function1dof.m

m = 12.319*0.25*0.036;
g = 386.1; % inch/s^2 
L = 8.6; Lc = L/2;
I = 0.653*2;

u = 0.5; % Torque input in lb-in

function func = F(t,x)
    func = zeros(2,1); 
    func(1) = x(2); 
    func(2) = (1/(Lc^2 + I))*(u - m*g*Lc*sin(x(1)));
end

Then, I created a second .m file, called solver1dof.m, to execute the ode45 command and (hopefully) solve the equation.

clear all
time_period = [0 2]; 
initial = [0, 0];
[t,x] = ode45(@F, time_period, initial);

However, running solver1dof.m gives an error claiming the function 'F' is undefined:

>> solver1dof
Undefined function or variable 'F'.

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in solver1dof (line 4)
[t,x] = ode45(@F, time_period, initial);

I am unsure on how to proceed, as it seems the function is perfectly well defined, as far as I can tell (obviously, it isn't).

Answer 1

[Steven Lord]

As stated in this documentation page, "Local functions are only visible within the file where they are defined, both to the script code and other local functions within the file. They are not visible to functions in other files, and cannot be called from the command line." The local function F defined inside the script file function1dof is not visible to script file solver1dof.

If you created a function handle to F inside function1dof, executed function1dof, and used that function handle variable inside solver1dof then the ode45 call inside solver1dof could start. But the variables defined in the script file function1dof are not visible inside the function F, so you will receive an error about an undefined function or variable Lc when ode45 tries to call F using the function handle.

Either move the definitions of those variables into F itself (at which point you might as well just make function1dof a function file rather than a script file) or define them in solver1dof and pass them into F as parameters.

[Chinmay Sridhar]

Thank you for the reply! I went with moving the definitions of the variables in function1dof into F as follows:

function func = F(t,x)
    m = 12.319*0.25*0.036;
    g = 386.1; % inch/s^2 
    L = 8.6; Lc = L/2;
    I = 0.653*2;
    u = 0.5; % Torque input in lb-in

    func = zeros(2,1); 
    func(1) = x(2); 
    func(2) = (1/(Lc^2 + I))*(u - m*g*Lc*sin(x(1)));
  end

Now, you mentioned I need to execute function1dof before I can call F inside of solver1dof, however, running this file gives me an error stating I do not have enough input arguments. I realize this is probably a simple error, but do you have any idea what I'm missing?

>> function1dof
Not enough input arguments.

Error in function1dof (line 9)
    func(1) = x(2);

[Steven Lord]

Now that you've made function1dof into a function file (its first executable line starts with the function keyword) you don't need to execute it first. However, know that MATLAB will know that function by the name function1dof (its file name) as opposed to F (the name used in the function declaration line.) When they differ, the file name trumps the function declaration line.

So you're going to need to use @function1dof in your ode45 call.

[Chinmay Sridhar]

It works now! Thank you for being patient, I realize these are very simple problems.