How to solve system of coupled second order linear differential equations in Matlab?

theta'' + 13.7786 x''+ (theta')^2=0;
-theta'' + 13.7786 y'' + (theta')^2=0;
0.5 theta''- x''(cos(theta))+y''(sin(theta))=0.24sin(theta);

1st Order and second order seperable equations are easy to solve, but in this case i don't know how can i solve it in Matlab.

• x =f1
• y =f2
• theta =f3
• x_dot =f4
• y_dot =f5
• theta_dot =f6
• x_dotdot =-(f6+diff(f6))/(13.7786)
• y_dotdot
• theta_dotdot

the problem is as you can see diff(f6) in x_dotdot, is it okay?

[Roger Stafford]

Your equations are linear with respect to all three second derivatives. Therefore, you can "solve" them as far as these second derivatives are concerned, obtaining something of the form:

theta'' = some expression involving theta' and theta
x'' = another expression involving theta' and theta
y'' = yet another expression involving theta' and theta

These results are all you need to call upon one of Matlab's 'ode' functions.

Answer 1

[Abraham Boayue]

I would recommend that you post your equations as an attachment. Problems of this form are usually not clear when written as a code.