Putting multiple equations into a function

Hey guys

I have four 1st order odes that I want to put into a function that will be later used with ode45. u1 = x1; u2 = dx1; u3 = x2; u4 = dx2

The equations go as following (These equations come from a two 2nd order odes):

du1 = dx1 = u2

du2 = d2x1 = -k1*(x1 - L1)/m1 + k2*(x2 - x1 - w1 - L2)/m1

du3 = dx2 = u4

du4 = d2x2 = -k2(x2 - x1 - w1 - L2)/m2

Where - L1 = L2 = 2; k1 = k2 = 5; m1 = m2 = 2; w1 = 5

The IC are - x1 = 2; x2 = L1 + w1 + L2 + 6

I have tried everything that I can think of but I have been getting the same error time after time and it is becoming very frustrating. Help would be greatly appreciated

Answer 1

[Zoltán Csáti]

Create this function:

function du = diffeq(t,u)
k1 = 5; k2 = 5;
m1 = 2, m2 = 2; w1 = 5;
L1 = -2; L2 = 2;
du = zeros(4,1);
du(1) = u(2);
du(2) = -k1/m1*(u(1)-L1) + k2/m1*(u(3)-u(1)-w1-L2);
du(3) = u(4);
du(4) = -k2/m2*(u(3)-u(1)-w1-L2);
end

Then invoke it with the appropriate solver (e.g. ode45):

L1 = -2; L2 = 2; w1 = 5;
[t u] = ode45(@diffeq, [0 10], [-2 0 L1+L2+w1+6 0]);

However note that you provided only 2 initial conditions instead of 4. Therefore I supposed the coordinate velocities to be zeroes.

[tyler brecht]

Thank you so very much! :). I could jump for joy, this work and yes the initial values for velocity are zero forgot to state it in my question. Thank you again

[Zoltán Csáti]

Here, you can find a large amount of materials about the built-in solvers and also how to write a higher order differential equation into a system of first order equations: http://www.mathworks.com/help/matlab/math/ordinary-differential-equations.html