Solving system of ODE's contains complex equations

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Iam forming system of 3 ODE's(dy1/dt, dy2/dt, dy3/dt) using matrices A, B and V.
A and B matrices(both 3*3) are interms of some variable teta.
I want to substitute y3 in place of teta and proceed solving ODE's.
My ODE is inv(B).*(V-(A*Y)), where V = column matrix of order 3.
i tried like this
syms teta
Ai = cos(teta).*([2 5 1;
7 9 0;
4 1 3])
Bi = sin(teta).*([1 2 3;
4 5 6;
7 8 9])
V = ones(3, 1)
odefun = @(t,Y) inv(B).*(V-(A*Y));
A = subs(Ai, teta, Y(3))
B = subs(Bi, teta, Y(3))
tspan = [0 10];
Y0=zeros(3,1);
[t, Y] = ode45(odefun, tspan, Y0);
Y1 = Y(:, 1);
hold on
plot(t, Y1);
Y2 = Y(:, 1);
plot(t, Y2);
Y3 = Y(:, 1);
plot(t, Y3);
legend('Y1','Y2','Y3')
But iam getting this error
Unrecognized function or variable 'Y'.
Error in Untitled5 (line 43)
A = subs(Ai, teta, Y(3))
Facing issue in substituting Y3, how to resolve that?
  4 Commenti
Bjorn Gustavsson
Bjorn Gustavsson il 30 Ago 2021
This surely makes, which you then attempt to invert?
Bathala Teja
Bathala Teja il 31 Ago 2021
I can avoid this by changing intial conditions.
My main question is how to solve this kind of problem. Dont consider values seriously.

Accedi per commentare.

Risposte (1)

Bjorn Gustavsson
Bjorn Gustavsson il 31 Ago 2021
The way it looks to me you have a problem something like this:
One problem is that the B-matrix you've given is singular which might be a problem. For problems like this there's not much need to doodle on with symbolic calculations, just implement the mass-matrix and ODE-function as matlab-functions and look for a numeric solution with ode45 or ode15s etc. Look at the help and documentation for those functions and focus in particular on the examples with mass-matrices. I'd figure the ODE-function would look something like:
function dydt = yourODE(t,y,A,V)
dydt = V - cos(y(3))*A*Y(:);
end
and the mass-matrix-function:
function M = yourMassM(t,y,B)
M = sin(y(3))*B;
end
Then you'll have to inform the ode-solver about the mass-matrix:
options = odeset('Mass',@(t,y) yourMassM(t,Y,B));
and then solve with some suitable initial conditions.
y0 = [pi/7,pi/11,pi/13];
t_span = [0,exp(17*pi)];
sol = ode15s(@(t,y) yourODE(t,y,A,V)),t_span,y0,options);
Since your mass-matrix is singular I dont guarantee that this works.
HTH

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