Vector ODE using forward Euler method

Having trouble defining the following vector ode in matlab.

I have written the following for the right hand side function for suitable use in ode45. The system models a projectile with position and velocity vectors (x(t), y(t)) and (u(t), v(t)) at time t with parameters g and mu for gravity and air resistance.

function dydt = rhs_1(t, y, g, mu)
dxdt1 = u;
dydt2 = v;
dudt3 = -mu.*y(1).*sqrt(y(1).^2+y(2).^2);
dvdt4 = -g-mu.*y(2).*sqrt(y(1).^2+y(2).^2);

dydt = [dxdt1, dydt2, dudt3, dvdt4];
end

And when I run the following;

[t,y,g,mu]=ode45(@rhs_1,[0 100],[0.1; 0], 9.8, 0.5);
plot(t,y,g,mu(:,1),'r.-',t,y(:,2),'g.-','LineWidth',2,'MarkerSize',10);

I get the following error messages;

Unrecognized function or variable 'u'.

Error in rhs_1 (line 2)
dxdt1 = u;

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 runode (line 1)
[t,y,g,mu]=ode45(@rhs_1,[0 100],[0.1; 0], 9.8, 0.5);

Apologies if this is trivial, I am new to Matlab. Any help is greatly appreciated. Thank you!

Answer 1

[Jan]

You have replaced the "x" of the formula by "y(1)", the "y" by "y(2)". Now you have to replace "u" by "y(3)" also and "v" by "y(4)":

function dydt = rhs_1(t, y, g, mu)
dxdt1 = y(3);  % instead of u
dydt2 = y(4);  % instead of v
dudt3 = -mu .* y(3) .* sqrt(y(3).^2 + y(4).^2);      % y(1) -> y(3), y(2) -> y(4)
dvdt4 = -g - mu .* y(4) .* sqrt(y(3).^2 + y(4).^2);
dydt  = [dxdt1, dydt2, dudt3, dvdt4];
end

Answer 2

[James Tursa]

Also your main code should look something like this:

g = 9.8;
mu = 0.5;
[t,y]=ode45(@(t,y)rhs_1(t,y,g,mu),[0 100],[0.1; 0]);

Then, depending on how you want your plotting, something like this:

plot(y(:,1),y(:,2));

or

plot(t,y(:,1),t,y(:,2));