How to solve these equations using ode45?

ok guys, I'm in a deep problem ... I need to solve equations below:

1.

2.

3.

4.

5.

6.

I have used ode45 before, but this one i can't figure out!

here is the equation that returns nothing :

clear, clc, close all;

%Load Initial Data
ACC=load('15 Imperial Valley El Centro 180.txt'); 
ag=9.8.*ACC(:,1); %m/s^2 horizontal ground acceleration 
dt=0.01; %s ground acceleration time step 
N=length(ag);
T=(N-1)*dt; %s ground acceleration duration 
t=0:dt:T; % time vector 

%Define Factors
dxdata = cumtrapz(t, ag);
xdata = cumtrapz(t, dxdata);

A = 1;
beta = 0.1;
gamma = 0.9;
n = 2;
mass = 10; %in g
Fy = 2.86; %in KN
Uy = 0.111; %in m
a = 0.1;
c = 0;
p = 2;
Ini_dx = dxdata(1);
Ini_x = xdata(1);
Ini_nou = 0;
Ini_eta = 0;
Ini_A = 1;
delta_nou = 0;
delta_eta = 0;
delta_psi = 0;
delta_A = 0;
Ini_zeta = 0;
psi = 0;
lambda = 0;
factor_q = 1;
factor_omega = sqrt(Fy/(mass * Uy));

[t,y] = ode45(@znew,t,[0 0 0],[],A,beta,gamma,n,mass,a,p,dxdata,xdata,Ini_nou,Ini_eta,Ini_A,delta_nou,delta_eta,delta_psi,delta_A,Ini_zeta,psi,lambda,factor_q,factor_omega);
z = y(:,2);
plot(t,z);

function out = znew(t,y,A,beta,gamma,n,mass,a,p,dxdata,xdata,Ini_nou,Ini_eta,Ini_A,delta_nou,delta_eta,delta_psi,delta_A,Ini_zeta,psi,lambda,factor_q,factor_omega)
    dut = interp1(dxdata,t,'spline');
    ut = interp1(xdata,t,'spline');
    z = y(2);
    out = zeros(3,1);
    epsilon = (1-a) * (factor_omega^2) * z * ut;
    out(1) = epsilon;
    noue = Ini_nou + delta_nou * epsilon;
    Ae = Ini_A - delta_A * epsilon;
    etae = Ini_eta + delta_eta * epsilon;
    zu = (1/(noue*(beta+gamma)))^(1/n);
    zeta1 = Ini_zeta * (1-exp(-p*epsilon));
    zeta2 = (psi + delta_psi * epsilon)*(lambda + zeta1);
    hzt = 1-zeta1*exp(-(((z * sign(dut)) - factor_q*zu)^2)/zeta2);
    dz = hzt * (Ae*dut - noue*(beta*abs(dut)*(abs(z)^(n-1))*z + gamma*dut*(abs(z)^n)))/etae;
    out(2) = z;
    out(3) = dz;
end

would appreciate some help guys ... not really good with ode45 :)

thanks in advance.

Answer 1

[Walter Roberson]

You are using an old syntax for ode45 that has not been documented for a decade. Please parameterize your function instead of counting on ode45 passing all those extra variables in.