Hello, I have divided first order differential equations into 6 systems over respective time span, I am getting result as Inputs must be floats, namely single or double. I have tried to correct but not happening. Please help

t1span=[0:0.5:pi]
t2span=[ pi:0.5:2*pi];
t3span=[ 2*pi:0.5:3*pi];
t4span=[3* pi:0.5:4*pi];
t5span=[4* pi:0.5:5*pi];
t6span=[5* pi:0.5:6*pi];
t=linspace(0,0.5,50)
Axis=[-30 100 -30 50]
x=linspace(-30,100,50)

x1= linspace(5.5,10.5,50)                       
x2=  linspace(10,14,50)                      

    t1span=[0:0.5:pi]
  t2span=[ pi:0.5:2*pi];
  t3span=[ 2*pi:0.5:3*pi];
  t4span=[3* pi:0.5:4*pi];
  t5span=[4* pi:0.5:5*pi];
  t6span=[5* pi:0.5:6*pi];
  t=linspace(0,0.5,50)
      k1=2; k2=7; xT=44;yT=32;
     xt=[ 2  7.18    12.77  17.53  20.87  28.68 ] ;  
       yt=[ 8 11.42  13.61  15.41  17.78  21.28 ];  

     q1=[q11;q21;q31]
     q10=[2; 8 ;0]
      %q20=[xt2 yt2 atan2(yt2-yt1,xt2-xt1)]
     % q20=[xt2 yt2 0.5826]
     q20=[ 7.1892; 11.4189 ;0.5826]
      q2=[q12 ;q22; q32] ;

     % q30=[xt3 yt3 atan2(yt3-yt2,xt3-xt2)]
    % q30=[xt3 yt3   0.3750]
    q30=[ 12.7734; 13.6167 ;0.3750]
      q3=[q13; q23 ;q33];
     % q40=[xt4 yt4 atan2(yt4-yt3,xt4-xt3)]
       %q40=[xt4 yt4 0.3620]
       q40=[17.522; 15.4147 ;0.3620]
      q4=[q14; q24; q34];
      %q50=[xt5 yt5 atan2(yt5-yt4,xt5-xt4)]
      % q50=[xt5 yt5 0.5988]
       q50=[21; 17.78; 0.5988]
      q5=[q15; q25; q35];
      %q60=[ xt6 yt6 atan2(yt6-yt5,xt6-xt5)]
       %q60=[ xt6 yt6 0.4264]
      q6=[q16; q26 ;q36];
      q60= [28.6819 ;  21.2781 ;0.4264]

       etheta31=atan2(32-8,44-2);
       etheta32=atan2(32-11.42,44-7.18);
       etheta33=atan2(32-13.61,44-12.77);
       etheta34=atan2(32-15.41,44-17.52);
       etheta35=atan2(32-17.78,44-21);
       etheta36=atan2(32-21.28,44-28.68);

v11= -k1*(44-2)
v12= -k1*(44-7.18)
v13= -k1*(44-12.77)
v14= -k1*(44-17.53)
v15= -k1*(xT-20.87)
  v16= -k1*(xT-28.86)
   v21=-k2*(atan2(32-8,44-2)+0.2)+(32-8)*sin(t1)
     v22=-k2*(atan2(32-11.42,44-7.18)-0.2)+(32-11.42)*sin(t2)
     v23=-k2*(atan2(32-13.61,44-12.77)-0.2)+(32-13.61)*sin(t3)
     v24=-k2*(atan2(32-15.41,44-17.52)-0.2)+(32-15.41)*sin(t4)
    v25=-k2*(atan2(32-17.78,44-21)-0.2)+(32-17.78)*sin(t5)
     v26=-k2*(atan2(32-21.28,44-28.68))+(32-21.28)*sin(t6)

       dq11dt1=v11*cos(q31);
       dq12dt2=v12*cos(q32);
       dq13dt3=v13*cos(q33);
       dq14dt4=v14*cos(q34);
       dq15dt5=v15*cos(q35);
       dq16dt6=v16*cos(q36);

       dq21dt1= v11*sin(q31);
       dq22dt2=v12*sin(q32);
       dq23dt3=v13*sin(q33);
       dq24dt4=v14*sin(q34);
       dq25dt5=v15*sin(q35);
       dq26dt6=v16*sin(q36);

       dq31dt1= v21;
        dq32dt2= v22;
        dq33dt3= v23;
        dq34dt4= v24;
        dq35dt5= v25;
        dq36dt6= v26;
        t1span=[0:0.5:pi];
          q1=[q11 q21 q31];
         q10=[2 8 0];

     F1=@(t1,q1)(vpa ([v11+v21*(32-8);-v21*(32-8);v21]));
     [t1,q1] = ode45(F1,t1span,q10);
        Plot (q11,q21)
             hold on; 

    q2=[q12 q22 q32]; 
    q20=[ 7.1892; 11.4189 ;0.5826]
    t2span=[ pi:0.5:2*pi];
    F2=@(t2,q2)(vpa([v12+v22*(32-11.42);-v22*(32-11.42);v22]));  
     [t2,q2] = ode45(F2,t2span,q20);
         plot(q12,q22)   
      hold on;

   q3=[q13 q23 q33]; 
   q30=[ 12.7734; 13.6167 ;0.3750];
   t3span=[2*pi:0.5:3*pi];
   F3=@(t3,q3)(vpa([v13+v23*(32-13.61);-v23*(32-13.61);v23]));  
  [t3,q3] = ode45(F3,t3span,q30);
       plot(q13,q23)
      hold on; 

   q4=[q14 q24 q34];  
   q40=[17.522; 15.4147 ;0.3620];
   t4span=[3*pi:0.5:4*pi];
     [t4,q4]    = ode45(F4,t4span,q40);
   F4=@(t4,q4)(vpa([v14+v24*(32-15.41);-v24*(32-15.41);v24]));     
         plot(q14,q24)
      hold on; 

q5=[q15 q25 q35];
q50=[21; 17.78; 0.5988];
t5span=[4*pi:0.5:5*pi];
    F5=@(t5,q5)(vpa([v15+v25*(32-17.78);-v25*(32-17.78);v25]));  
     [t5,q5] = ode45(F5,t5span,q50);
         plot(q15,q25)
    hold on; 

   q6=[q16 q26 q36]; 
   q60= [28.6819 ;  21.2781 ;0.4264]
   t6span=[5*pi:0.5:6*pi];
     F6=@(t6,q6)(vpa([v16+v26*(32-21.28);-v22*(32-21.28);v26]));  
    [t6,q6] = ode45(F6,t6span,q60);
          plot(q16,q26)
     hold off;

end

Answer 1

[Walter Roberson]

Several of your variables are undefined, especially your t* and q* variables.

You have

       F1=@(t1,q1)(vpa ([v11+v21*(32-8);-v21*(32-8);v21]));

vpa() returns a symbolic value even if the inputs are numeric. ode45() cannot work with symbolic values.

I suspect you have defined the q* variables and t* variables as symbolic. Please note that when you have equations along the line of

   syms x
   y = x^2;
   F = @(x) y

then when F is evaluated, there is no connection made between the x of the input argument and the x that appears in the formula for y.

You should probably be creating your F1 by using

F1 = matlabFunction([v11+v21*(32-8);-v21*(32-8);v21], 'vars', [t1, q1])

[sangita kamat]

Thanks Walter, I will try as per your suggestion and revert back

[sangita kamat]

I am still stuck up with above problem, tried as per above ,but it comes as variables undefined