Why do I receive 'not enough input arguments' in ode45

Hello all,

I am trying to find the solution to a N links system with Lagrange constraints, using ode45. I have defined the relevant matrices and formatted them as matlabFunction for the ode45 to use.

When calling the ode45 function I repeatedly get the following error:

Not enough input arguments.

Error in symengine>@(u1,u2,u3,u4,u5,v1,v2,v3,v4,v5,theta1,theta2,theta3,theta4,theta5,u_d1,u_d2,u_d3,u_d4,u_d5,v_d1,v_d2,v_d3,v_d4,v_d5,theta_d1,theta_d2,theta_d3,theta_d4,theta_d5)[0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;0.0;theta1.*2.0-theta2;-theta1+theta2.*2.0-theta3;-theta2+theta3.*2.0-theta4;-theta3+theta4.*2.0-theta5;-theta4+theta5]

Error in not_working>odefcn4 (line 109)

Gtemp=G(z);

Error in not_working (line 69)

[t,z] = ode45(@(t,z) odefcn4(t,z,M,G,C,W,Wd), tint, IC);

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

My code is as follows:

clc;close all;

N=5;

syms u [1 N] real

syms u_d [1 N] real

syms v [1 N] real

syms v_d [1 N] real

syms theta [1 N] real

syms theta_d [1 N] real

syms m I k c w d l delta L v0 t_sym real

svars= [m I k c w d l delta L v0];

L_val=2; v0_val=1;

vars=[1 1 1 1 1 1 N/L_val 0.2 2 1];

q=[u v theta]; %DOF vector, length 3*N

q_d=[u_d v_d theta_d]; %DOF derivative vector

T=sum(m/2.*(u_d.^2+v_d.^2)+I/2.*(theta_d).^2); %Kinetic Energy

V=0.5*k*theta1^2;

for i=2:N

V= V+0.5*k*(theta(i)-theta(i-1))^2; % Potential Energy

end

D=sum(0.5*c.*theta_d.^2); %Dissipation Energy

h=sym(zeros(1,2*N+2));

h(1)=u1-d/2;

h(1+N)=v1-v0*t_sym-w/2;

h(1+2*N)=theta1;

for i=2:N

h(i)=u(i)-u(i-1)-(l/2)*cos(theta(i))-(l/2)*cos(theta(i-1));

h(i+N)=v(i)-v(i-1)-(l/2)*sin(theta(i))-(l/2)*sin(theta(i-1)); %Constraints, length 2*N+2

end

h(2*N+2)=d/2+L-delta-(u(N)+(l/2)*cos(theta(N)));

W=sym(zeros(length(h),length(q)));

Wd=sym(zeros(length(h),length(q)));

for i=1:length(h)

W(i,:)=gradient(h(i),q);

for j=1:length(q)

Wd(i,j)=gradient(W(i,j),q)'*q_d';

end

end

M=hessian(T,q_d);

G=gradient(V,q);

C=gradient(D,q_d); %Lagrangian formulation

M=double(subs(M,svars,vars));

G=matlabFunction(subs(G,svars,vars),'Vars',[q q_d]);

C=matlabFunction(subs(C,svars,vars),'Vars',[q q_d]);

W=matlabFunction(subs(W,svars,vars),'Vars',[q q_d]);

Wd=matlabFunction(subs(Wd,svars,vars),'Vars',[q q_d]);

tint=[0 10];

IC=zeros(1,6*N);

IC(1,3*N+1)=v0_val;

IC(1,1:N)=(0:L_val/N:L_val-L_val/N)+L_val/(2*N);

[t,z] = ode45(@(t,z) odefcn4(t,z,M,G,C,W,Wd), tint, IC);

and the function odefcn4 is deifned as:

function dzdt = odefcn4(t,z,M,G,C,W,Wd) % Isolating the second derivative part of the constraints equation

N=length(M(1,:)/3);

Gtemp=G(z);

Ctemp=C(z);

Wtemp=W(z);

Wdtemp=Wd(z);

LHS=zeros(5*N+2,5*N+2);

LHS(1:3*N,1:3*N)=M;

LHS(1:3*N,(3*N+1):5*N+2)=-Wtemp';

LHS((3*N+1):(5*N+2),1:3*N)=Wtemp;

RHS=zeros((5*N+2),1);

RHS(1:3*N,1)=-Ctemp-Gtemp;

RHS((3*N+1):(5*N+2),1)=-Wdtemp*z(1:(3*N))';

eq=LHS\RHS;

dzdt=[z((3*N+1):(5*N+2)); eq(1:3*N)];

end

Thank you for your help

[Torsten]

Did you look at the list of input parameters to M,G,C,W and Wd after transforming them to functions with the "matlabFunction" command ? This calling list must be used when you call the functions in odefcn4.

Answer 1

[Walter Roberson]

G=matlabFunction(subs(G,svars,vars),'Vars', {[q q_d]} );
C=matlabFunction(subs(C,svars,vars),'Vars', {[q q_d]} );
W=matlabFunction(subs(W,svars,vars),'Vars', {[q q_d]} );
Wd=matlabFunction(subs(Wd,svars,vars),'Vars', {[q q_d]} );