I get this error:"This system does not seem to be linear."

When I try this code for simple pendulum, I get results:

syms pt(t) th(t)
m=1; l=0.5; g=9.81;
e1= diff(th)*(m*l^2)==pt;
e2= diff(pt)==-m*g*l*sin(th);
vars = [pt(t); th(t)];
V = odeToVectorField([e1,e2]);
M = matlabFunction(V, 'vars', {'t','Y'});
interval = [0 5];
y0 = [0; pi/4];
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2),1000);

a= deval(ySol,tValues,1)/(m*l^2);
plot(tValues,a)

But when I use it for triple pendulum, it gives error. Couldn't solve it. Sorry if it's simple to figure out. Really new here.

syms theta1(t) theta2(t) theta3(t) p1(t) p2(t) p3(t)
m1=1; m2=1; m3=1; l1=1; l2=1;
 l3=1; g=9.81; tau1=0; tau2=0; tau3=0;
 I1=0; I2=0; I3=0;
 e1= diff(theta1)*(I1+(m1+m2+m3)*l1^2)...
     +diff(theta2)*(m2+m3)*l1*l2*cos(theta1-theta2)+...
     diff(theta3)*m3*l1*l3*cos(theta1-theta3)==p1;
 e2= diff(theta1)*(m2+m3)*l1*l2*cos(theta1-theta2)+...
     diff(theta2)*(I2+(m2+m3)*l2^2)+...
     diff(theta3)*m3*l2*l3*cos(theta2-theta3)==p2;
 e3= diff(theta1)*m3*l1*l3*cos(theta1-theta3)+...
     diff(theta2)*m3*l2*l3*cos(theta2-theta3)+...
     diff(theta3)*(I3+m3*l3^2)==p3;
 e4= diff(p1)== tau1-tau2-(m2+m3)*diff(theta1)*diff(theta2)*sin(theta1-theta2)...
     -m3*diff(theta1)*diff(theta3)*l1*l3*sin(theta1-theta3)...
     -(m1+m2+m3)*g*l1*cos(theta1);
 e5= diff(p2)==tau2-tau3+(m2+m3)*diff(theta1)*theta2*l1*l2*sin(theta1-theta2)...
     -m3*diff(theta2)*diff(theta3)*l2*l3*sin(theta2-theta3)...
     -(m2+m3)*g*l2*cos(theta2);
 e6= diff(p3)==tau3+(m3)*diff(theta1)*diff(theta3)*l1*l3*sin(theta1-theta3)...
     +m3*diff(theta2)*diff(theta3)*l2*l3*sin(theta2-theta3)...
     -m3*g*l3*cos(theta3);
 vars= [theta1(t);theta2(t);theta3(t);p1(t);p2(t);p3(t)];
 V = odeToVectorField([e1,e2,e3,e4,e5,e6]);
 M = matlabFunction(V,'vars', {'t','Y'});

I have get that error in simple pendulum too, it was pt==diff(th)*(m*l^2), then I put the pt to the end, and it's solved. In triple pendulum I tried leaving diff(theta1) alone didn't work, tried to this code too, but nothing changed. Original equations are:

Answer 1

[Torsten]

The product of differentials in your equations (diff(theta1)*diff(theta3), e.g.) makes it impossible to use ODE45.

I don't know if it can be applied directly, but ODE15I is the correct solver to use in this case.

Best wishes

Torsten.

[Arda Nova]

I see, I will look it up, thank you.

[Arda Nova]

Hi, I tried what you have said, it worked on simple pendulum (I alway start with simple pendulum to see if I can). Here is the codes for simple pendulum:

function res = odennotfun(~,y,yp)
m=2; l=3; g=9.81
res=[yp(1)+m*g*l*sin(y(2));
y(1)-m*l^2*yp(2);];%%y1Pt y2te yp1pdte yp2ted
end

y0 = [0; pi/2];
yp0=[0; 0];
[y0,yp0] = decic(@odennotfun,0,y0,[0 pi/2],yp0,[]);
[t,y] = ode15i(@odennotfun,[0 10],y0,yp0);
plot(t,y(:,1)/2/3)

This works fine. Then I tried, the other code.

function hell2 = odennotfunatall(~,y,yp)
m1=1; m2=1; m3=1; l1=1; l2=1;
 l3=1; g=9.81; tau1=0; tau2=0; tau3=0; I1=0; I2=0; I3=0;
hell2=[yp(1)*(I1+(m1+m2+m3)*l1^2)...
     +yp(2)*(m2+m3)*l1*l2*cos(y(1)-y(2))+...
     yp(3)*m3*l1*l3*cos(y(1)-y(3))-y(4);
 yp(1)*(m2+m3)*l1*l2*cos(y(1)-y(2))+...
     yp(2)*(I2+(m2+m3)*l2^2)+...
     yp(3)*m3*l2*l3*cos(y(2)-y(3))-y(5);
 yp(1)*m3*l1*l3*cos(y(1)-y(3))+...
     yp(2)*m3*l2*l3*cos(y(2)-y(3))+...
     yp(3)*(I3+m3*l3^2)-y(6);
 -yp(4)+tau1-tau2-(m2+m3)*yp(1)*yp(2)*sin(y(1)-y(2))...
     -m3*yp(1)*yp(3)*l1*l3*sin(y(1)-y(3))...
     -(m1+m2+m3)*g*l1*cos(y(1));
 -yp(5)+tau2-tau3+(m2+m3)*yp(1)*yp(2)*l1*l2*sin(y(1)-y(2))...
     -m3*yp(2)*yp(3)*l2*l3*sin(y(2)-y(3))...
     -(m2+m3)*g*l2*cos(y(2));
 -yp(6)+tau3+(m3)*yp(1)*yp(3)*l1*l3*sin(y(1)-y(3))...
     +m3*yp(2)*yp(3)*l2*l3*sin(y(2)-y(3))...
     -m3*g*l3*cos(y(3));];
end

y0 = [pi/2; pi/2; pi/2; 0; 0; 0];
yp0=[0; 0; 0; 0; 0; 0;];
[y0,yp0] = decic(@odennotfunatall,0,y0,[pi/2 pi/2 pi/2 0 0 0],yp0,[]);
[t,y] = ode15i(@odennotfunatall,[0 5],y0,yp0);
plot(t,y)

And it gave out problem:

>> Notfunatall_ans
Error using vertcat
Dimensions of matrices being concatenated are not consistent.

Error in odennotfunatall (line 4)
hell2=[yp(1)*(I1+(m1+m2+m3)*l1^2)...

Error in decic (line 66)
res = feval(odefun,t0,y0,yp0,varargin{:});

Error in Notfunatall_ans (line 3)
[y0,yp0] = decic(@odennotfunatall,0,y0,[pi/2 pi/2 pi/2 0 0 0],yp0,[]);
 

Can you pinpoint the problem? it is just weird. It should work but doesn't.

[Torsten]

function main
y0 = [pi/2; pi/2; pi/2; 0; 0; 0];

yp0=[0; 0; 0; 0; 0; 0;];

[y0,yp0] = decic(@odennotfunatall,0,y0,[pi/2 pi/2 pi/2 0 0 0],yp0,[]);

[t,y] = ode15i(@odennotfunatall,[0 5],y0,yp0);

plot(t,y)
end

function hell2 = odennotfunatall(~,y,yp)

m1=1; m2=1; m3=1; l1=1; l2=1;

 l3=1; g=9.81; tau1=0; tau2=0; tau3=0; I1=0; I2=0; I3=0;

 hell2=zeros(6,1);
hell2(1)=yp(1)*(I1+(m1+m2+m3)*l1^2)...
     +yp(2)*(m2+m3)*l1*l2*cos(y(1)-y(2))+...
     yp(3)*m3*l1*l3*cos(y(1)-y(3))-y(4);

 hell2(2)=yp(1)*(m2+m3)*l1*l2*cos(y(1)-y(2))+...
     yp(2)*(I2+(m2+m3)*l2^2)+...
     yp(3)*m3*l2*l3*cos(y(2)-y(3))-y(5);

 hell2(3)=yp(1)*m3*l1*l3*cos(y(1)-y(3))+...
     yp(2)*m3*l2*l3*cos(y(2)-y(3))+...
     yp(3)*(I3+m3*l3^2)-y(6);

 hell2(4)=-yp(4)+tau1-tau2-(m2+m3)*yp(1)*yp(2)*sin(y(1)-y(2))...
     -m3*yp(1)*yp(3)*l1*l3*sin(y(1)-y(3))...
     -(m1+m2+m3)*g*l1*cos(y(1));

 hell2(5)=-yp(5)+tau2-tau3+(m2+m3)*yp(1)*yp(2)*l1*l2*sin(y(1)-y(2))...
     -m3*yp(2)*yp(3)*l2*l3*sin(y(2)-y(3))...
     -(m2+m3)*g*l2*cos(y(2));

 hell2(6)=-yp(6)+tau3+(m3)*yp(1)*yp(3)*l1*l3*sin(y(1)-y(3))...
     +m3*yp(2)*yp(3)*l2*l3*sin(y(2)-y(3))...
     -m3*g*l3*cos(y(3));

end

[Arda Nova]

Yeah the zeros, couldn't find a way to put it, thank you very much.

Answer 2

[madhan ravi]

Just follow the same way showed in your previous question?

[Arda Nova]

I did the same. And it worked on simple pendulum. Doing the exactly the same thing on the triple pendulum and it gives the error. Sorry by the way, I hate asking this much questions, normally I hate asking questions, I always try to learn own my own, but due time is too close this time, though I have given up on the project. This time it just baffles me, that doing the same thing gives a different result. Maybe crazy people are not that crazy after all :D.

[madhan ravi]

No problem , please recheck your equations take your time there are only four equations whereas you have 6 equations in your code.

[Arda Nova]

Oh sorry, upper picture is streched out. At the right of "(60)" (on the picture), there is two more equations.