call large equation to ode solver

dear all

i want solve equation with using ode113

clc
clear all
tic
initialcond=[-0.001,-0.001,-0.001,-0.001,-0.001,-0.001]
[T X]=ode113(@solver2link,[0 40],initialcond);
toc

this is my ode file and the following file is my equation

function dy = shebhestatici1(t,y)
X1=y(1,1);
X2=y(2,1);X3=y(3,1);X4=y(4,1);X5=y(5,1);X6=y(6,1);
M 
G
xdd=inv(M)*(-G);
dy=xdd;                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
end

i calculate M and G from different file

previously M and G are short equation and i could copy theme directly to my ode solver

but now after some changes it become large file and i cant copy them

so my question is how could i call them to my ode solver for example :

    function dy = shebhestatici1(t,y)
    X1=y(1,1);
    X2=y(2,1);X3=y(3,1);X4=y(4,1);X5=y(5,1);X6=y(6,1);
  function M G
  xdd=inv(M)*(-G);
  dy=xdd;                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
  end

i know its wrong but just to clear my point

thank you all

Answer 1

[Torsten]

function dy = shebhestatici1(t,y)
    X1=y(1,1);
    X2=y(2,1);
    X3=y(3,1);
    X4=y(4,1);
    X5=y(5,1);
    X6=y(6,1);
    M = function_where_you_supply_M(X1,X2,X3,X4,X5,X6);
    G = function_where_you_supply_G(X1,X2,X3,X4,X5,X6);
    xdd=-M\G;
    dy=xdd;
end

[shahin hashemi]

ty mr torsten for your answer but i cant understand what do you mean by the where_you_supply_M

this is code where i calculate M and G

    clc
     clear all
    m=7.782e-4;
    jx=2.011E-14;
    E=2.1e11;
    O=0.008;
    jz=1.149e-13;
    G=8e10;
    L=0.09;
    g=9.81;
    N=4;
    T1=0;
    T2=0;
    T3=0;
    Ixx=9.821e-8;
    Izz=1.654e-7;
    %  syms L m jx E O jz G L g Ixx Izz T1 T2 T3
    % syms T1 T2 T3

    xd = sym('xd', [1 3*N], 'real');
    xdd = sym('xdd', [1 3*N], 'real');
    x  = sym(zeros(1,3*N));%preallocation
    syms t
    for i=1:3*N
       x(i)=sym(sprintf('x%d(t)',i), 'real');
    end

    rl(:,:,1)=[1*O;0;0;];
    rl(:,:,2)=[(-1/2)*O;(sqrt(3))*O/2;0];
    rl(:,:,3)=[(-1/2)*O;-(sqrt(3))*O/2;0];
    for j=2:N+1
       for i=j-1
    f1(:,:,j)=(1-cos(x(3*i-2)))/x(3*i-2);
    g1(:,:,j)=-(1-cos(x(3*i-1)))/x(3*i-1);
    f2(:,:,j)=sin(x(3*i-2))/x(3*i-2);
    g2(:,:,j)=sin(x(3*i-1))/x(3*i-1);
    f1d(:,:,j)=(sin(x(3*i-2))*x(3*i-2)+cos(x(3*i-2))-1)/(x(3*i-2)^2);
    g1d(:,:,j)=-(sin(x(3*i-1))*x(3*i-1)+cos(x(3*i-1))-1)/(x(3*i-1)^2);
    f2d(:,:,j)=(cos(x(3*i-2))*x(3*i-2)-sin(x(3*i-2)))/(x(3*i-2)^2);
    g2d(:,:,j)=(cos(x(3*i-1))*x(3*i-1)-sin(x(3*i-1)))/(x(3*i-1)^2);
    pl(:,:,j)=L*[f1(:,:,j) f2(:,:,j)*g1(:,:,j) f2(:,:,j)*g2(:,:,j)]';
    Rl(:,:,j)=[cos(x(3*i))*cos(x(3*i-2)) -sin(x(3*i))*cos(x(3*i-2)) sin(x(3*i-2));cos(x(3*i))*sin(x(3*i-2))*sin(x(3*i-1))+sin(x(3*i))*cos(x(3*i-1)) -sin(x(3*i))*sin(x(3*i-2))*sin(x(3*i-1))+cos(x(3*i))*cos(x(3*i-1)) -cos(x(3*i-2))*sin(x(3*i-1));-cos(x(3*i))*sin(x(3*i-2))*cos(x(3*i-1))+sin(x(3*i))*sin(x(3*i-1)) sin(x(3*i))*sin(x(3*i-2))*cos(x(3*i-1))+cos(x(3*i))*sin(x(3*i-1)) cos(x(3*i-2))*cos(x(3*i-1))];
    p(:,:,2)=pl(:,:,2);
       end
    end

        R(:,:,2)=Rl(:,:,2);
        R(:,:,1)=[1 0 0;0 1 0;0 0 1];

    for i=3:N+1
        R(:,:,i)=R(:,:,i-1)*Rl(:,:,i);
        p(:,:,i)=p(:,:,i-1)+R(:,:,i-1)*pl(:,:,i);
    end

    for j=2:N+1
        for i=j-1
    wl(:,:,j)=[sin(x(3*i-2))*(diff(x(3*i), t))+diff(x(3*i-1),t);-cos(x(3*i-2))*sin(x(3*i-1))*(diff(x(3*i), t))+cos(x(3*i-1))*(diff(x(3*i-2), t));cos(x(3*i-2))*cos(x(3*i-1))*(diff(x(3*i), t))+sin(x(3*i-1))*(diff(x(3*i-2), t))];
    w(:,:,2)=wl(:,:,2);
        end
    end
    for i=3:N+1
        w(:,:,i)= w(:,:,i-1)+R(:,:,i-1)*wl(:,:,i);
    end
     for j=2:N+1
          for i=j-1
      pd(:,:,j)=L*[f1d(:,:,j) 0 0;f2d(:,:,j)*g1(:,:,j) f2(:,:,j)*g1d(:,:,j) 0;f2d(:,:,j)*g2(:,:,j) f2(:,:,j)*g2d(:,:,j) 0]*[(diff(x(3*i-2), t));(diff(x(3*i-1), t));(diff(x(3*i), t))];
      v(:,:,2)=pd(:,:,2);
          end
     end
     for i=3:N+1
         v(:,:,i)=v(:,:,i-1)+cross(w(:,:,i-1),R(:,:,i-1)*pl(:,:,i))+R(:,:,i-1)*pd(:,:,i);
     end
     for j=2:N+1
    wdlcl(:,:,j)=diff(wl(:,:,j),t);
    alfa(:,:,2)=wdlcl(:,:,2);
     end
    for i=3:N+1
        alfa(:,:,i)= alfa(:,:,i-1)+cross(w(:,:,i-1),R(:,:,i-1)*wl(:,:,i))+R(:,:,i-1)*wdlcl(:,:,i);
    end
    for i=2:N+1
        for j=1:N
    alfa(:,:,i)=subs(alfa(:,:,i),(diff(x(3*j), t)),xd(3*j));
    alfa(:,:,i)=subs(alfa(:,:,i),(diff(x(3*j-1), t)),xd(3*j-1));
    alfa(:,:,i)=subs(alfa(:,:,i),(diff(x(3*j-2), t)),xd(3*j-2));
    alfa(:,:,i)=subs(alfa(:,:,i),(diff(x(3*j), t,t)),xdd(3*j));
    alfa(:,:,i)=subs(alfa(:,:,i),(diff(x(3*j-1), t,t)),xdd(3*j-1));
    alfa(:,:,i)=subs(alfa(:,:,i),(diff(x(3*j-2), t,t)),xdd(3*j-2));
        end 
    end
     for j=2:N+1
    pdd(:,:,j)=diff(pd(:,:,j),t);
    a(:,:,2)=pdd(:,:,2);
     end
     for i=3:N+1
     a(:,:,i)= a(:,:,i-1)+cross(diff(w(:,:,i-1),t),R(:,:,i-1)*pl(:,:,i))+cross(2*w(:,:,i-1),R(:,:,i-1)*pd(:,:,i))+cross(w(:,:,i-1),cross(w(:,:,i-1),R(:,:,i-1)*pl(:,:,i-1)))+R(:,:,i-1)*pdd(:,:,i);
     end
    for i=2:N+1
        for j=1:N
    a(:,:,i)=subs(a(:,:,i),(diff(x(3*j), t)),xd(3*j));
    a(:,:,i)=subs(a(:,:,i),(diff(x(3*j-1), t)),xd(3*j-1));
    a(:,:,i)=subs(a(:,:,i),(diff(x(3*j-2), t)),xd(3*j-2));
    a(:,:,i)=subs(a(:,:,i),(diff(x(3*j), t,t)),xdd(3*j));
    a(:,:,i)=subs(a(:,:,i),(diff(x(3*j-1), t,t)),xdd(3*j-1));
    a(:,:,i)=subs(a(:,:,i),(diff(x(3*j-2), t,t)),xdd(3*j-2));
    w(:,:,i)=subs(w(:,:,i),(diff(x(3*j), t)),xd(3*j));
    w(:,:,i)=subs(w(:,:,i),(diff(x(3*j-1), t)),xd(3*j-1));
    w(:,:,i)=subs(w(:,:,i),(diff(x(3*j-2), t)),xd(3*j-2));
    v(:,:,i)=subs(v(:,:,i),(diff(x(3*j), t)),xd(3*j));
    v(:,:,i)=subs(v(:,:,i),(diff(x(3*j-1), t)),xd(3*j-1));
    v(:,:,i)=subs(v(:,:,i),(diff(x(3*j-2), t)),xd(3*j-2));
        end 
    end 
     for i=2:N+1
        Fi(:,:,i)=-m*a(:,:,i); 
     end
     for i=2:N+1
        Ii(:,:,i)=R(:,:,i)*[Ixx 0 0;0 Ixx 0;0 0 Izz]*transpose(R(:,:,i));
        Mi(:,:,i)=-Ii(:,:,i)*alfa(:,:,i)-cross(w(:,:,i),Ii(:,:,i)*w(:,:,i));
     end

     for i=2:N+1
           wk(:,:,i)=jacobian(w(:,:,i),[xd(1),xd(2),xd(3)  ,xd(4),xd(5),xd(6),xd(7),xd(8),xd(9),xd(10),xd(11),xd(12)]);% ,xd(13),xd(14),xd(15),xd(16),xd(17),xd(18),xd(19),xd(20),xd(21),xd(22),xd(23),xd(24)]);
     end
     for i=2:N+1
            vk(:,:,i)=jacobian(v(:,:,i),[xd(1),xd(2),xd(3)  ,xd(4),xd(5),xd(6),xd(7),xd(8),xd(9),xd(10),xd(11),xd(12)]);%,xd(13),xd(14),xd(15),xd(16),xd(17),xd(18),xd(19),xd(20),xd(21),xd(22),xd(23),xd(24)]);
    end
     for j=N+1
      for i=j-1
      Mb(:,:,j)=E*jx*((x(3*i-1))/L)*R(:,:,j-1)*[1;0;0]+E*jx*((x(3*i-2))/L)*R(:,:,j-1)*[0;1;0];
      Mt(:,:,j)=-G*jz*(x(3*i))*R(:,3,j)/L;
      Me(:,:,j)=Mt(:,:,j)-Mb(:,:,j);
      end
    end
    for j=2:N+1
        for i=j-1
      Mb(:,:,j)=E*jx*((x(3*i-1))/L)*R(:,:,j-1)*[1;0;0]+E*jx*((x(3*i-2))/L)*R(:,:,j-1)*[0;1;0];
        end
    end
    for j=2:N
        for i=j-1
    Mt(:,:,j)=-G*jz*(x(3*i))*R(:,3,j)/L;
        end
    end
    for j=2:N
         for i=j
    Mtt(:,:,j)=G*jz*(x(3*i))*R(:,3,j)/L;
         end
    end
    for j=N+1
        Mtt(:,:,j)=[0;0;0];
    end
    for i=2:N+1
        MT(:,:,i)=Mt(:,:,i)+Mtt(:,:,i);
    end
    for  i=2:N
        Me(:,:,i)=Mb(:,:,i+1)-Mb(:,:,i)+MT(:,:,i);
    end
    for i=2:N+1
        Fg(:,:,i)=-m*g*[1;0;0]; 
    end
    for i=2
    ph(:,1,i)=[pl(:,:,i)+R(:,:,i)*rl(:,:,1)-rl(:,:,1)];
    ph(:,2,i)=[pl(:,:,i)+R(:,:,i)*rl(:,:,2)-rl(:,:,2)];
    ph(:,3,i)=[pl(:,:,i)+R(:,:,i)*rl(:,:,3)-rl(:,:,3)];
    end
    for i=3:N+1
    ph(:,1,i)=[R(:,:,i-1)*pl(:,:,i)-R(:,:,i-1)*rl(:,:,1)+R(:,:,i)*rl(:,:,1)];
    ph(:,2,i)=[R(:,:,i-1)*pl(:,:,i)-R(:,:,i-1)*rl(:,:,2)+R(:,:,i)*rl(:,:,2)];
    ph(:,3,i)=[R(:,:,i-1)*pl(:,:,i)-R(:,:,i-1)*rl(:,:,3)+R(:,:,i)*rl(:,:,3)];
    end

    for i=2:N+1
    ap(:,:,i)=[sqrt((ph(1,1,i))^2 + (ph(2,1,i))^2 + (ph(3,1,i))^2 );sqrt((ph(1,2,i))^2 + (ph(2,2,i))^2 + (ph(3,2,i))^2);sqrt((ph(1,3,i))^2 + (ph(2,3,i))^2 + (ph(3,3,i))^2)];
    f(:,:,i)=[ph(:,1,i)/ap(1,1,i) ph(:,2,i)/ap(2,1,i) ph(:,3,i)/ap(3,1,i) ];
    end

    for i=N+1 
        Fc(:,:,i)=[-T1*f(:,1,i) -T2*f(:,2,i) -T3*f(:,3,i) ]; 
    end

    for i=2:N
        Fc(:,:,i)=[T1*(f(:,1,i+1)-f(:,1,i)) T2*(f(:,2,i+1)-f(:,2,i)) T3*(f(:,3,i+1)-f(:,3,i)) ];
    end

    for i=2:N+1
       fa(:,:,i)=Fc(:,1,i)+Fc(:,2,i)+Fc(:,3,i);
    end

    for i=2:N+1
        Ma(:,:,i)=cross(R(:,:,i)*rl(:,:,1),Fc(:,1,i))+cross(R(:,:,i)*rl(:,:,2),Fc(:,2,i))+cross(R(:,:,i)*rl(:,:,3),Fc(:,3,i));
    end

    for i=2:N+1 
        feq(:,:,i)=fa(:,:,i)+Fg(:,:,i)+Fi(:,:,i); 
        Meq(:,:,i)=Ma(:,:,i)+Me(:,:,i)+Mi(:,:,i); 
    end
    for j=1:(3*N)   
        for i=2:N+1
         FF(j,i-1)= dot(Meq(:,:,i),wk(:,j,i))+dot(feq(:,:,i),vk(:,j,i));
        end
    end
    for j=1:(3*N)
        F(j,1)=sum(FF(j,:));
    end

     for i=1:3*N
    M(i,:)=jacobian(F(i,1),[xdd(1),xdd(2),xdd(3)  ,xdd(4),xdd(5),xdd(6),xdd(7),xdd(8),xdd(9),xdd(10),xdd(11),xdd(12)]);%,xdd(13),xdd(14),xdd(15),xdd(16),xdd(17),xdd(18),xdd(19),xdd(20),xdd(21),xdd(22),xdd(23),xdd(24)]);
     end

    % % for i=1:3*N
    % %     for j=1:N
    % % F(i,1)=subs(F(i,1),xd(3*j), 0);
    % % F(i,1)=subs(F(i,1),xd(3*j-1), 0);
    % % F(i,1)=subs(F(i,1),xd(3*j-2), 0);
    % %     end 
    % % end
    % %  for i=1:3*N
    % % M(i,:)=jacobian(F(i,1),[xdd(1),xdd(2),xdd(3)  ,xdd(4),xdd(5),xdd(6)]);%,,xdd(7),xdd(8),xdd(9),xdd(10),xdd(11),xdd(12)]);%,xdd(13),xdd(14),xdd(15),xdd(16),xdd(17),xdd(18),xdd(19),xdd(20),xdd(21),xdd(22),xdd(23),xdd(24)]);
    % %  end
    % %
    % %  test M ba F dar zamane jacobian
    GG=F;
     for i=1:3*N
        for j=1:N
    GG(i,1)=subs(GG(i,1),xd(3*j), 0);
    GG(i,1)=subs(GG(i,1),xd(3*j-1), 0);
    GG(i,1)=subs(GG(i,1),xd(3*j-2), 0);
    GG(i,1)=subs(GG(i,1),xdd(3*j), 0);
    GG(i,1)=subs(GG(i,1),xdd(3*j-1), 0);
    GG(i,1)=subs(GG(i,1),xdd(3*j-2), 0);
        end 
     end
     X = sym('X', [1 3*N], 'real');
     for i=1:3*N
        for j=1:N
    GG(i,1)=subs(GG(i,1),x(3*j),X(3*j));
    GG(i,1)=subs(GG(i,1),x(3*j-1),X(3*j));
    GG(i,1)=subs(GG(i,1),x(3*j-2), X(3*j));
        end 
     end
      for i=1:3*N
          for j=1:N
    M(i,:)=subs(M(i,:),x(3*j),X(3*j));
    M(i,:)=subs(M(i,:),x(3*j-1),X(3*j));
    M(i,:)=subs(M(i,:),x(3*j-2), X(3*j));
          end
     end

and i save this file with the name of shebhestatici1 can you tell me that what changes should i do ?

[shahin hashemi]

i should mention that GG and G are the same thank you again

[Torsten]

Make your code a function with output argments G and M and call it from where you need M and G.

[shahin hashemi]

i can change my code to a function but just with one output

 function M  = shebhestatici1
.
.
.
.
end

how should i do that for 2 ?

maybe like this ?

this doesnt work

function [M G] = shebhestatici1

and for last question should i put smth in front of shebhestatici1 ?

like :

function M  = shebhestatici1(x)

[Torsten]

https://de.mathworks.com/help/matlab/ref/function.html

In your case:

function [M,G] = shebhestatici1

If X1,...,X6 are needed to generate M and G,

function [M,G] = shebhestatici1(X1,X2,X3,X4,X5,X6)

Best wishes

Torsten.