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

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Syed hamza Ali Tirmizi 2018-3-29

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https://ww2.mathworks.cn/matlabcentral/answers/391518-how-to-solve-system-of-coupled-second-order-linear-differential-equations-in-matlab

编辑： Syed hamza Ali Tirmizi 2018-3-30

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?

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Roger Stafford 2018-3-30

在 MATLAB Online 中打开

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.

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