Trying to solve 4 coupled differential equations using ode45 and keep getting the error not enough input arguments

function Q2a
m0 = 120000;
n = 15;
mf = m0/n;
Isp = 320;
g = 9.81;
T = 1.4*m0*g;
me = T/(Isp*g);
t0 = 0;
tb = (m0 - mf)/me;
tspan = [t0 tb];
gamma0 = 1.568;
m = [m0 mf];
ht = 110;

function dvdt = velocity(t,g,T,m,gamma0,ht,littlegam)
while alt <= ht
dvdt = (T - m*g*sin(gamma0))/m ; 
end
while alt > ht 
dvdt = (T - m*g*sin(littlegam))/m;
end
end

function [t,v] = vel(tspan,g,T,m,gamma0,ht,littlegam,t)
v0 = 0;
[t,v] = ode45(@(t,m) velocity(t,g,T,m,gamma0,ht,littlegam) ,tspan , v0);
output(t,v)
end

function dhdt = altitude(t,vel,littlegam,ht,gamma0)
v = vel;
while ht >= alt 
dhdt=v.*sin(gamma0);
end
while alt > ht
dhdt = v.*sin(littlegam);
end
end

function [t,h] = alt(tspan, vel, littlegam, ht, gamma0)
h0 = 0;
[t,h] = ode45(@(t,vel) altitude(t,vel,littlegam,ht,gamma0) , tspan, h0);
end

function dgammadt = pitch_angle(t,g0,littlegam,vel,Re,alt,gamma0,ht)
h = alt;
v = vel;
while ht >= alt
dgammadt=(-(1./v)).*(g0-((v.^2)./(Re+h))).*(cos(gamma0));
end
while alt > ht
dgammadt=(-(1./v)).*(g0-((v.^2)./(Re+h))).*(cos(littlegam));
end
end

function [t,gamma] = littlegam(g0,alt,Re,vel,gamma0,tspan,ht)
[t,gamma] = ode45(@(t,vel) pitch_angle(t,g0,littlegam, vel, Re, alt, gamma0, ht) , tspan, gamma0);
end 

function dxdt = downrange_dist(Re,alt,vel,littlegam,ht,gamma0,t)
while ht >= alt
dxdt=(Re./(Re+ h)).*v.*cos(gamma0);
end
while alt > ht
dxdt=(Re./(Re+ alt)).*vel.*cos(littlegam);
end
end

function [t,x] = dis(Re,alt,vel,littlegam,tspan,ht,gamma0)
x0 = 0;
[t,x] = ode45(@(t,alt) downrange_dist(Re,alt,vel,littlegam,ht,gamma0,t), tspan, x0);
end

plot(tspan,vel);
plot(tspan,alt);
plot(tspan,littlegam);
plot(tspan,dis);

end

[Sonny Whittley]

Not enough input arguments.

Error in Q2a/vel (line 27) [t,v] = ode45(@velocity ,tspan , v0);

Error in Q2a (line 77) plot(tspan,vel);

>> Sorry my bad, here is the full error message

Answer 1

[Jan]

Please post the complete error message. This would reveal the failing line and is much better than letting the readers guess, where the code fails.

As far as I can see, the code has a general flaw. E.g.:

      while alt <= ht
         dvdt = (T - m*g*sin(gamma0))/m ;
      end

This is an infinite loop, because alt is not changed inside it. Maybe you mean if alt <= ht.

The actual error occurs in this line:

plot(tspan, vel)

Here the function vel() is called without inputs, but actually your require:

vel(tspan,g,T,m,gamma0,ht,littlegam,t)

I do not understand the purpose of the code. But usually coupled ODEs are handled very differently. Please read the documentation again:

 doc ode45   % See the examples there
 doc while

Note that your function to be integrated seems to have a discontinuity at ht=alt, but Matlab's ODE integrators handle smooth functions only, see http://www.mathworks.com/matlabcentral/answers/59582#answer_72047. Use an event function instead to stop the integration at this ht value and restart it with the modified formula.

[Sonny Whittley]

Thanks for your help, ill make your changes and hopefully it works. This code is supposed to solve the 4 coupled differential equations to enable me to plot a rocket's dynamic parameters against time.

[Torsten]

And why don't you solve all 4 differential equations together in one call to ODE45, but in 4 separate calls ? I even think that you must solve them all together since you state that they are coupled.

[Sonny Whittley]

I have previously tried to solve them all together and my graphs all just stayed constant at 0.