ode45 Inputs must be floats, namely single or double.

I Have this code and I do not know where is the problem. I end up with:

Error in ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in SixDOFSolutionOnlyFromMaple (line 7)
[t, D]=ode45(@SixDOF14March2019,range,IC);

This is the code (Matlab function) and I want to make it easy for you to follow:

1) I have 5 ODEs which are second order.

2) The 5 ODE varibles are (x, y , z, thx, thy) and their derivatives (xdot, ydot, zdot, thxdot, thydot)

3) I did the summation to calculate some forces.

4) I noticed some thing strang (not sure if it has any effect) that when I want to calculate (DelAL) and the 3 other varibles above it I end up with an expression includes cos(%1) and somethings like that! I do NOT know what is (%1)??!!

function der=SixDOF14March2019(t,D)


x=D(1);
xdot=D(2);
y=D(3);
ydot=D(4);
z=D(5);
zdot=D(6);
thx=D(7);
thxdot=D(8);
thy=D(9);
thydot=D(10);
%thz=D(11);
%thzdot=D(12);
%clear all; close all; clc; format long;

syms x y z thx thy thz xdot ydot zdot thxdot thydot thzdot t Fr Fa J


syms lR lL 
syms RjInR RjOutR RjInL RjOutL 
syms rIn rOut 
syms B
syms thj
syms thinitial 
syms alphaO alphaP 
syms Pr deltaP Zp 
syms omIn omOut omC omB n 
syms Nin Nout Nball 
syms AjInA AjInRad AjOutA AjOutRad 
syms AInA AInRad AOutA AOutRad 
syms Ainitial 
syms psi 
syms Ajb Ab 
syms RjOutRFinal RjInRFinal RjOutFinal RjInLFinal 
syms DeltajR DelatajAR DeltajRR DeltajL DelatajAL DeltajRL 
syms alphajR alphajL 
syms deltajR deltajL 
syms rgIn rgOut dIn dOut db dm m 
syms gamma fin fo SigRhoIn SigRhoOut FRhoIn FRhoOut
syms Ein Eout Eb newIn newOut newB DeltaStarIn DeltaStarOut 
syms gammaInitial SigRhoInInitial SigRhoOutInitial FRhoInInitial FRhoOutInitial DeltaStarInInitial DeltaStarOutInitial KInInitial KOutInitial 
syms DeltaStarInjR DeltaStarInjL DeltaStarOutjR DeltaStarOutjL 
syms M 
syms Ix Iy Iz 
syms C 

% GIVEN:
% ======
g=9.81;
lR=0.1275; lL=0.0875;
rgIn=0.00408;rgOut=0.00461;dIn=0.046; dOut=0.062;db=0.00794;dm=0.5*(dIn+dOut);m=6;
alphaO=15*pi/180;
Ein=(2.07*10^11);Eout=(2.07*10^11);Eb=(2.07*10^11);newIn=0.3;newOut=0.3;newB=0.3;
M=5.5;
Ix=0.05177; Iy=Ix; Iz=0.0044;
psi=0;thinitial=0;
AInA=0;AOutA=0;AInRad=0;AOutRad=0;Ab=0; 
Ainitial=0;
Nin=0;Nout=0;Nball=0;
Pr=50;
n=2500; 
omIn=(2*pi*n/60);omOut=0;
B=rgIn+rgOut-db; 
alphaP=.273932890990504;

Us = 0.217e-1; Ud = 1.3;

C=300; 


%INITIAL CALCULATIONS USING alphaO%
%==================================

gammaInitial=db*cos(alphaO)/dm;
fi=rgIn/db; fo=rgOut/db;

FRhoInInitial= ((1/fi)+(2*gammaInitial/(1-gammaInitial)))/((4)-(1/fi)+(2*gammaInitial/(1-gammaInitial)));
FRhoOutInitial= ((1/fo)-(2*gammaInitial/(1+gammaInitial)))/((4)-(1/fo)-(2*gammaInitial/(1+gammaInitial)));

SigRhoInInitial=(1/db)*((4)-(1/fi)+(2*gammaInitial/(1-gammaInitial)));
SigRhoOutInitial=(1/db)*((4)-(1/fo)-(2*gammaInitial/(1+gammaInitial)));

% DeltaStarInInitial
if (FRhoInInitial>=0)&&(FRhoInInitial<0.9) 
    DeltaStarInInitial=(-4.473235689079742*(FRhoInInitial^6))+(10.221093192616578*(FRhoInInitial^5))+(-9.137566232244472*(FRhoInInitial^4))+(3.727561235805512*(FRhoInInitial^3))+(-0.911658734913609*(FRhoInInitial^2))+(0.041760021004309*(FRhoInInitial))+(0.999977423957012);
elseif (FRhoInInitial>=0.9)&&(FRhoInInitial<=0.995)
    DeltaStarInInitial=(-0.178413900461346*(10^6)*(FRhoInInitial^5))+(0.836143462688479*(10^6)*(FRhoInInitial^4))+(-1.567353804615937*(10^6)*(FRhoInInitial^3))+(1.468900655521535*(10^6)*(FRhoInInitial^2))+(-0.688261350489303*(10^6)*(FRhoInInitial))+(0.128985184237206*(10^6));
elseif (FRhoInInitial>0.995)&&(FRhoInInitial<=1)
    DeltaStarInInitial=(-0.283909265667587*(10^12)*(FRhoInInitial^5))+(1.414016787576658*(10^12)*(FRhoInInitial^4))+(-2.817011913800072*(10^12)*(FRhoInInitial^3))+(2.806027557873945*(10^12)*(FRhoInInitial^2))+(-1.397540196512594*(10^12)*(FRhoInInitial))+(0.278417030529744*(10^12));
end

% DeltaStarOutInitial
if (FRhoOutInitial>=0)&&(FRhoOutInitial<0.9) 
    DeltaStarOutInitial=(-4.473235689079742*(FRhoOutInitial^6))+(10.221093192616578*(FRhoOutInitial^5))+(-9.137566232244472*(FRhoOutInitial^4))+(3.727561235805512*(FRhoOutInitial^3))+(-0.911658734913609*(FRhoOutInitial^2))+(0.041760021004309*(FRhoOutInitial))+(0.999977423957012);
elseif (FRhoOutInitial>=0.9)&&(FRhoOutInitial<=0.995)
    DeltaStarOutInitial=(-0.178413900461346*(10^6)*(FRhoOutInitial^5))+(0.836143462688479*(10^6)*(FRhoOutInitial^4))+(-1.567353804615937*(10^6)*(FRhoOutInitial^3))+(1.468900655521535*(10^6)*(FRhoOutInitial^2))+(-0.688261350489303*(10^6)*(FRhoOutInitial))+(0.128985184237206*(10^6));
elseif (FRhoOutInitial>0.995)&&(FRhoOutInitial<=1)
    DeltaStarOutInitial=(-0.283909265667587*(10^12)*(FRhoOutInitial^5))+(1.414016787576658*(10^12)*(FRhoOutInitial^4))+(-2.817011913800072*(10^12)*(FRhoOutInitial^3))+(2.806027557873945*(10^12)*(FRhoOutInitial^2))+(-1.397540196512594*(10^12)*(FRhoOutInitial))+(0.278417030529744*(10^12));
end


KInInitial=((4*2^0.5)/3)*(1/(SigRhoInInitial)^0.5)*((Ein*Eb)/(Ein+Eb-(Ein*newB^2)-(Eb*newIn^2)))*(1/DeltaStarInInitial)^1.5
KOutInitial=((4*2^0.5)/3)*(1/(SigRhoOutInitial)^0.5)*((Eout*Eb)/(Eout+Eb-(Eout*newB^2)-(Eb*newOut^2)))*(1/DeltaStarOutInitial)^1.5

KInitial=(1/(((1/KInInitial)^(2/3))+((1/KOutInitial)^(2/3))))^(3/2)


Zp=B*(sin(alphaP-alphaO)/cos(alphaP));


omB=(0.5*dm*db)*((omIn*(1-(db*cos(alphaO)/dm)^2))+(omOut*(1+(db*cos(alphaO)/dm)^2)));
omC=(0.5)*((omIn*(1-(db*cos(alphaO)/dm)))+(omOut*(1+(db*cos(alphaO)/dm))));
thj=(omC*t)+((2*pi*(J-1))/m)+thinitial;
     

AjInA=(AInA*sin(Nin*(psi+(omC-omIn)*t+(2*pi*(j-1)/m))))+Ainitial;
AjOutA=(AOutA*sin(Nout*(psi+(omC-omOut)*t+(2*pi*(j-1)/m))))+Ainitial;

AjInRad=(AInRad*sin(Nin*(psi+(omC-omIn)*t+(2*pi*(j-1)/m))))+Ainitial;
AjOutRad=(AOutRad*sin(Nout*(psi+(omC-omOut)*t+(2*pi*(j-1)/m))))+Ainitial;

Ajb=2*Ab*sin(Nball*omB*t);


DelRadR=B*cos(alphaO)+x*cos(thj)+y*sin(thj)-lR*thy*cos(thj)+lR*thx*cos(thy)*sin(thj)+(1/2)*dm*cos(thj)*(1-cos(thy))+(1/2)*dm*sin(thj)*(1-cos(thx));
DelRadL=B*cos(alphaO)+x*cos(thj)+y*sin(thj)-lL*thy*cos(thj)+lR*thx*cos(thy)*sin(thj)-(1/2)*dm*cos(thj)*(1-cos(thy))-(1/2)*dm*sin(thj)*(1-cos(thx));
DelAR=B*sin(alphaO)+Zp+z+lR*(1-cos(thy))*cos(thj)+lR*(1-cos(thx))*cos(thy)*sin(thj)-(1/2)*thy*dm*cos(thj)+(1/2)*thx*dm*sin(thj);
DelAL=B*sin(alphaO)+Zp-z+lL*(1-cos(thy))*cos(thj)+lL*(1-cos(thx))*cos(thy)*sin(thj)+(1/2)*thy*dm*cos(thj)-(1/2)*thx*dm*sin(thj);


alphajR = atan(DelAR/DelRadR);
alphajL = atan(DelAL/DelRadL);


deltajR = (DelAR^2+DelRadR^2)^.5+Ajb-B;
deltajL = (DelAL^2+DelRadL^2)^.5+Ajb-B;

% (Initial) Forces:
% =========================

QR = KInitial*deltajR^1.5;
FxR = QR*cos(alphajR)*cos(thj);
FyR = QR*cos(alphajR)*sin(thj);
FzR = QR*sin(alphajR);
MxR = FyR*lR+(1/2)*FzR*sin(thj)*dm;
MyR = FxR*lR+(1/2)*FzR*cos(thj)*dm;

FxxR = symsum(FxR, J, 1, m)
FyyR = symsum(FyR, J, 1, m)
FzzR = symsum(FzR, J, 1, m)
MxxR = symsum(MxR, J, 1, m)
MyyR = symsum(MyR, J, 1, m)


QL = KInitial*deltajL^1.5;
FxL = QL*cos(alphajL)*cos(thj);
FyL = QL*cos(alphajL)*sin(thj);
FzL = QL*sin(alphajL);
MxL = FyL*lL+(1/2)*FzL*sin(thj)*dm;
MyL = FxL*lL+(1/2)*FzL*cos(thj)*dm;

FxxL = symsum(FxL, J, 1, m)
FyyL = symsum(FyL, J, 1, m)
FzzL = symsum(FzL, J, 1, m)
MxxL = symsum(MxL, J, 1, m)
MyyL = symsum(MyL, J, 1, m)

% (Initial) Equations:
% ====================
der=[xdot;
    (-1/M)*(C*xdot+FxxR+FxxL-M*g-Us*omIn^2*cos(omIn*t));
    ydot;
    (-1/M)*(C*ydot+FyyR+FyyL-Us*omIn^2*sin(omIn*t));
    zdot;
    (-1/M)*(C*zdot+FzzR+FzzL);
    thxdot;
    (-1/Ix)*(Iz*thydot*omIn+MxxL-MxxR- Ud*omIn^2*cos(omIn*t));
    thydot;
    (-1/Iy)*(-Iz*thxdot*omIn+MyyL-MyyR- Ud*omIn^2*sin(omIn*t))];

This is the solution code:

clear all; close all; clc; format long;

range=[0 0.1];
IC=[10e-6 0 10e-7 0 10e-8 0 0 0 0 0];


[t, D]=ode45(@SixDOF14March2019,range,IC);

Your participation is greatly appreciated!

[Steven Lord]

You omitted the top of the error and/or warning stack. Please post all the red and/or orange text, as it will likely contain information that will be useful in determining the cause of the failure.

[darova]

2.  x=D(1);
...
15.   syms x y z 
...
100. DelRadR=B*cos(alphaO)+x*cos(thj)+y*sin(thj)-lR*thy*cos(thj)+lR*thx*cos(thy)*sin(thj)+(1/2)*dm*cos(thj)*(1-cos(thy))+(1/2)*dm*sin(thj)*(1-cos(thx));
101. DelRadL=B*cos(alphaO)+x*cos(thj)+y*sin(thj)-lL*thy*cos(thj)+lR*thx*cos(thy)*sin(thj)-(1/2)*dm*cos(thj)*(1-cos(thy))-(1/2)*dm*sin(thj)*(1-cos(thx));

Create new script and type:

x = 5;
syms x
disp(x)

[Hassan Alkomy]

Error using odearguments (line 113)
Inputs must be floats, namely single or double.

Error in ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in SixDOFSolutionOnlyFromMaple (line 7)
[t, D]=ode45(@SixDOF14March2019,range,IC);

I am sorry, this is the complete error.

[Hassan Alkomy]

Hi Darova,

I do not know what is your point?

what you did is not clear for me.

Sorry for that.

[darova]

All values you pass der must be numeric

xdot = D(2);        % first you assign xdot value from D(2)
syms xdot           % then you declare xdot as symbolic variable
der = [xdot];       % trying to pass symbolic variable

[Hassan Alkomy]

Thank you @darova. The code works well now.