Second Order Differential Equations to 2 First Order

I'm trying to turn <http://latex.codecogs.com/gif.latex?\frac{\mathrm{d^2}%20\theta%20}{\mathrm{d}%20t^2}%20=%20-sin\theta> to 2 first order differential equations so I can then use ode45 to solve them. With initial conditions theta(0)=0.1 and theta primed(0)=0, <http://latex.codecogs.com/gif.latex?\frac{\mathrm{d}%20\theta%20}{\mathrm{d}%20t}=%200>

Here is my attempt at it:

function xprime=first(t,x);

xprime(1)=x(2);

xprime(2)=-sin(x);

xprime=xprime(:);

I save this as a mfile.

Then use :

ts[1,10];
x0 = [0 1]
[t,s] = ode45('first',ts,x0);

I get the error :

n an assignment A(I) = B, the number of elements in B and I must be the same.

Error in ==> first at 5 xprime(2)=-sin(x);

Now I have no clue how to correct this problem. I followed the guide here http://www.mathworks.com/support/tech-notes/1500/1510.html#reduce to no avail.

Anyone got any ideas? This is the first question on my assignment questions and the rest require this to be correct so am totally stuck at the moment.

Thanks in advance.

Answer 1

[Andrew Newell]

The problem is that in

xprime(2)=-sin(x);

the LHS is a scalar while the RHS is a vector. I think what you need is

xprime(2)=-sin(x(1));

[Matt Tearle]

This is indeed the problem. I just want to add that it's nicer to use a function handle to pass the rate equations to ODE45:

[t,s] = ode45(@first,[t0,tf],x0);