Solve system of ode

Question

Jeroen 2014-4-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/126902-solve-system-of-ode

回答： Sara 2014-4-24

Hi,

Last week I tried to experiment with the ode45 function. Now I can solve just a simple ode. But now I have a system with 4 degrees of freedom. Those will be y = [x(t) v(t) theta(t) omega(t)] which represent the distance, velocity, angle and angular velocity of a rolling cilinder.

Can you guys please help me solving this ?

I seperated all the ode's in 4 different ones with the following result:

y' - v(t) - (Fcm/m) = 0

y' + (Cx/m)*x(t) - (Cx*r/m)*theta(t) = 0

y' - omega(t) = 0

y' - (Cx*R/Iy)*x(t) + (Cx*R^2/Iy)*theta(t) = 0

These equations are the result of a matrix A (4x4) times a vector y (4x1) equals dy/dt

Can you guys please help me out solving this?

Thanks in advance

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Answer 1

Sara 2014-4-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/126902-solve-system-of-ode#answer_134397

在 MATLAB Online 中打开

How to call the solver:

[t,Y] = ode45(@(t,x)sisdif(t,x,Fcm,m,Cx,r,R,Iy),[t0 t1],initialConditions);

where [t0 t1] is the integration interval initialConditions is a 4by1 array with the initial condition

Function (check the signs to be sure I did it right):

function dy = sisdif(t,y,Fcm,m,Cx,r,R,Iy)
x = y(1);
v = y(2);
theta = y(3);
omega = y(4);
dy = zeros(4,1);
dy(1) = v + (Fcm/m)
dy(2) = - (Cx/m)*x + (Cx*r/m)*theta
dy(3) = + omega
dy(4) = + (Cx*R/Iy)*x - (Cx*R^2/Iy)*theta