Writing a system of ODEs for ode45

Hi,

I wrote a .m-file that has three second-order differential equations, broken down into six first-order equations.

When I run the code, I get the error message, "Unrecognized function or variable 'y'.

Here's the beginning of my code file:

x = y(1);
y = y(2);
theta = y(3);
vx = y(4);
vy = y(5);
omega = y(6);
g = 9.81;           % gravitational acceleration

Another question is: should I write a function file, or use anonymous function handles?

Thanks!

[Paul]

Hi Noob,

You're more likely to get an answer if you post the complete code and the error message. From what's shown

x = y(1);
y = y(2);   % <- problem here
theta = y(3);
vx = y(4);
vy = y(5);
omega = y(6);
g = 9.81;           % gravitational acceleration

there will be a problem after the indicated line because y is being reassigned as a scalar value from y(2), but the next line references y(3) for the assignment to theta. But, based on the error message it sounds like you're having a different error before you get to this portion of the code.

Answer 1

[Sam Chak]

Hi @Noob,

Your code is unfinished, and when you run it, MATLAB will throw an error message. You can also try solving the ODE by creating an ode object function. See example below. This method was introduced in release R2023b. For more information, please check out this link:

https://www.mathworks.com/help/matlab/ref/ode.html

F = ode;
F.Parameters = 9.81;
F.ODEFcn = @(t, y, g) [y(4);                % dx/dt
                       y(5);                % dy/dt
                       y(6);                % dtheta/dt
                     - y(4) - g*sin(y(1))   % dvx/dt
                     - y(5) - g*sin(y(2))   % dxy/dt
                     - y(6) - g*sin(y(3))]; % domega/dt
F.InitialValue = [3 2 1 0 0 0];             % x0, y0, theta0, vx0, vy0, omega0
% F.Solver     = "ode45";                   % default automatically selects a solver
sol = solve(F, 0, 10);                      % solve ode in the time interval from 0 to 10

% Plotting the results
plot(sol.Time, sol.Solution), grid on
legend({'$x$', '$y$', '$\theta$', '$v_{x}$', '$v_{y}$', '$\omega$'}, 'interpreter', 'latex', 'fontsize', 12, 'location', 'southeast')
xlabel('Time (seconds)')