how to solve nonlinear coupled dgl second order

Hello everyone,

Does anybody know how to solve the following two differential equotations using ODE45?

My Problem is, that i don't know how to rewrite the phi'' and x'' during the transformation in a system of dgl's first order.

Thanks

[Christian Dieterich]

g, l and the masses mw and mk are constant. Fan and Fr can leave away.

Answer 1

[Abraham Boayue]

Here is an example that I have obtained using ode45; the solution seems quite logical since we a dealing with sine waves.

clear variables
close all
N = 500;
L = 5; g = 9.81; mw = 2; mk = 5; Fan = 4; FR = 2;
q1 = -1/L;
q2 = -g/L;
F1 = -(mk*L)/(mw + mk);
F2 = -F1;
S = (Fan - FR)/(mw + mk);
F = @(t,y) [ y(2) ; 
    (1./(1-q1*F1*(cos(y(1)).^2))).*(0.5*q1*F2*sin(2*y(1)).*y(2).^2+...
        q1*S*cos(y(1)) + q2*sin(y(1)))];
 t0 = -2*pi;
tf = 2*pi;
tspan = t0:(tf-t0)/(N-1):tf;
ic = [0 0];
[t,y] = ode45(F, tspan, ic);
figure
plot(t,y(:,1),'-o')
hold on
plot(t,y(:,2),'-o')
a = title('\theta vs \theta_{prime}');
legend('\theta','\theta_{prime}');
set(a,'fontsize',14);
a = ylabel('y');
set(a,'Fontsize',14);
a = xlabel('t [-2\pi 2\pi]');
set(a,'Fontsize',14);
xlim([t0 tf])
grid
grid minor;

Answer 2

[Abraham Boayue]

Can you provide some values for the constants?

[Christian Dieterich]

Hello Abraham Boayue,

First of all, Thanks for your help. Let's say that mw is 1000 kg and mw is 10 kg. L is 1 m and the initial condition of x' und x are 0, the initial condition of phi' is 0 and the initial condition of phi is 0.4 rad.

Answer 3

[Abraham Boayue]

[Christian Dieterich]

Thanks!!!!! This is my last hope!