MATLAB: Ode23 , matrix equation , 2nd order DE

2nd order dematrix equationode23

How I will solve this matrix in Matlab ?
w=10.02;
p= 7850;     %%%Kg/m^3;
g=9.81;
G=77*10^9;        %%% N/m^2

E=206*10^9;       %%% N/m^2
L=9.6;   %%%m
D=0.15 ; %%m
m=pi*(D/2)^2*L*p;
A=pi*D^2/4 ; %%m2
J=m*D^2/8;  %%Kg*m^2
Ip=pi*D^4/32 ;   %% m^4
I=pi*D^4/64 ; 
cx=0.05*m*w;
cy=0.05*m*w;
ct=0.08*J*w;
kx=3*E*I/L;
ky=3*E*I/L;
kt=G*Ip/L;

Best Answer

You can find roots for x'', y'' and dtheta'' every iteration solving matrix equation
function du = func(t,u)
    u1 = u(1:3)';                        % [x y theta]'
    du1 = u(4:6)';                       % [dx dy dtheta]'
    dth = u(6);                          % dtheta
    C = [cx 0 0; 0 cy 0; 0 0 cz];        % C matrix
    K = ...                              % K matrix
    F = [me(w+dth)^2+Fx; ...]            % force vector
    A = [m 0 -mesin(wt)...]              % mass matrix
    B = -C*du1 -K*u1 + F;                
    du = zeros(6,1);
    du(1:3) = u(4:6);
    du(4:6) = A\B;
end
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