Convert symbolic system of differential Equations to numerical for ODE45

Hi all. I have to solve a FEM Problem. For this I created a function which computes the needed matrices and so the set of differential equations. The output of this function is a symbolc vector dy which contains the set of differential equations which are functions of y already in state-space representation. It looks like:

 dy = [y5*cos(y3)....;y3*sin(y3)...;...]

I want to read this symbolic vector into a function file say "cylinder_DGL". I already made the computation for an easy problem where the set of differential equations is computed in advance with Mathematica. It looks like:

function dy = cylinder_DGL(t,y,time_r,dt,ug,vg,Sys)
% CYLINDER_DGL evaluates the equation of motion for the rocking and rolling
% cylinder for given time instants t, excitation ug and vg and system
% properties R and H
% Save geometry properties into new variables
r = Sys.r;
h = Sys.h;
g=9.81;
% Interpolate the excitation ug and vg for the time instant t
i = floor(t/dt);
if i < length(time_r)
  u = ug(i) + (t-time_r(i))/(time_r(i+1)-time_r(i))*(ug(i+1)-ug(i));
  v = vg(i) + (t-time_r(i))/(time_r(i+1)-time_r(i))*(vg(i+1)-vg(i));
else
  u = 0;
  v = 0;
end
% Evaluate the equation of motion with help of the state space
% formulation
% State space formulation: row 1
dy(1,1)= y(2);
% State space formulation: row 2
dy(2,1)= ((4/3*h^2 - 5/4*r^2) * y(4)^2 * cos(y(1)) * sin(y(1))...
  + 3/2*r^2 * y(4)^2 * sin(y(1)) + h*r * y(4)^2 * (1+cos(y(1)))...
  - 2*h*r * y(4)^2 * cos(y(1))^2 - r*g * cos(y(1)) + h*g * sin(y(1))...
  - h*u * cos(y(3))*cos(y(1)) - r*u * cos(y(3))*sin(y(1))...
  - h*v * cos(y(1))*sin(y(3)) - r*v * sin(y(3))*sin(y(1)))...
  /(5/4*r^2 + 4/3*h^2);
% State space formulation: row 3
dy(3,1)= y(4);
% State space formulation: row4
dy(4,1)= (-3*r^2 * y(2)*y(4)*sin(y(1))...
  + (5/2*r^2-8/3*h^2)*y(2)*y(4)*sin(y(1))*cos(y(1))...
  - 4*h*r*y(2)*y(4)*(sin(y(1))^2+cos(y(1))-1)...
  - r*v*cos(y(3))*(1-cos(y(1))) - r*u*sin(y(3))*(1-cos(y(1)))...
  - h*v*sin(y(1))*cos(y(3)) + h*u*sin(y(3))*sin(y(1)))...
  / ((4/3*h^2 - 5/4*r^2)*sin(y(1))^2 + 3*r^2*(1-cos(y(1)))...
     + 2*h*r*sin(y(1))*(1-cos(y(1))));
end

This can then be started from the script with:

 refine = 4; 
        options = odeset('Events',@events_overturn,'Refine', refine,...
            'RelTol', 1e-9,'absTol',1e-9*[1 1 1 1]);
        % Solve the equations of motion
        [t,y,te,ye,ie] = ode45(@(t,y) ...
            cylinder_DGL(t,y,time_r,dt,ug,vg,Sys),t_3D,IC,options);

How can I read in the symbolic vector dy into my cylinder_DGL file and convert it so that I can use it to be started from the script as for the easy problem?

[Star Strider]

I don’t see that you’re using the Symbolic Math Toolbox anywhere.

In any event, two functions that can help turn a symbolic expression for your ODE into code you can run with the ODE solvers are odeToVectorField and matlabFunction.