منبع : mathworks.ir

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% simple pendelum - rung-kutta method

% saeed babanezhad

clc

clear all

%-----------------

g=9.8;

L=1;

N=200;

w=sqrt(g/L);

t=linspace(0,5,N); % time between 0-5s

h=t(2)-t(1);   % time step

f=@(alpha) alpha;

g=@(teta) -w^2*sin(teta);

teta=zeros(1,N);

alpha=zeros(1,N);

teta(1)=10*pi/180;   % initial angle(radian)

alpha(1)=0;          % initial angle speed

for i=1:N-1

k1= f(alpha(i));

kp1= g(teta(i));

k2=f(alpha(i)+h/2*kp1);

kp2=g(teta(i)+h/2*k1);

k3=f(alpha(i)+h/2*kp2);

kp3=g(teta(i)+h/2*k2);

k4=f(alpha(i)+h*kp2);

kp4=g(teta(i)+h*k2);

teta(i+1)=teta(i)+h/6*(k1+2*k2+2*k3+k4);

alpha(i+1)=alpha(i)+h/6*(kp1+2*kp2+2*kp3+kp4);

end

plot(t,teta)