Question

MATLAB code for a double pendulum. Please explain each lines for these codes pls.

----------------------------------------------------------------------------
clc
close all
clear all

%---------Parameters------------------------------------------------------

L1=1; L2=1 ; M_1=2 ; M_2=1; G=9.8;

%---------initial condition-----------------------------------------------

tspan=30;
theta1=3;
theta1_prime=0;
theta2=2.5;
theta2_prime=0;

y0=[theta1 theta1_prime theta2 theta2_prime];
[t,y]=ode45(@pend, [0 ,tspan],[ 3 0 2 0]);

%---position of mass 1 and mass 2----------------------------------------

x1=L1*sin(y(:,1));
y1=-L1*cos(y(:,1));
x2=L1*sin(y(:,1))+l2*sin(y(:,3));
y2=-L1*cos(y(:,1))-l2*cos(y(:,3));

%------visualizing the result---------------------------------------------

figure(1)
plot(x1,y1,'linewidth',2)
hold on
plot(x2,y2,'r','linewidth',2)
h=gca;
get(h,'fontSize')
set(h,'fontSize',14)
xlabel('X','fontSize',14);
ylabel('Y','fontSize',14);
title('Chaotic Double Pendulum','fontsize',14)
fh = figure(1);
set(fh, 'color', 'white');

figure(2)
plot(y(:,1),'linewidth',2)
hold on
plot(y(:,3),'r','linewidth',2)
h=gca;
get(h,'fontSize')
set(h,'fontSize',14)
legend('\theta_1','\theta_2')
xlabel('time','fontSize',14);
ylabel('theta','fontSize',14);
title('\theta_1(t=0)=2.5 and \theta_2(t=0)=1.0','fontsize',14)
fh = figure(2);
set(fh, 'color', 'white');


%----movie of double pendulum--------------------------------------

figure(3)
Ncount=0;
fram=0;

for i=1:length(y)
Ncount=Ncount+1;
fram=fram+1;
plot(0, 0,'.','markersize',20);
hold on
plot(x1(i),y1(i),'.','markersize',20);
plot(x2(i),y2(i),'.','markersize',20);
hold off
line([0 x1(i)], [0 y1(i)],'Linewidth',2);
axis([-(L1+l2) L1+l2 -(L1+l2) L1+l2]);
line([x1(i) x2(i)], [y1(i) y2(i)],'linewidth',2);
h=gca;
get(h,'fontSize')
set(h,'fontSize',12)
xlabel('X','fontSize',12);
ylabel('Y','fontSize',12);
title('Chaotic Motion','fontsize',14)
fh = figure(3);
set(fh, 'color', 'white');
F=getframe;
end

movie(F,fram,20)
  
%-----------------------------------------------------------------------   

Answer 1

Following is the explanation of each line. I have commented against the lines

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

%-------------- Double Pendulum--------------------------------------------

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

clc

close all

clear all

%---------Parameters------------------------------------------------------

l1=1; l2=2 ; m1=2 ; m2=1; g=9.8;

%---------initial condition-----------------------------------------------

tspan=50;

theta1=1.6;

theta1_prime=0;

theta2=2.2;

theta2_prime=0;

y0=[theta1 theta1_prime theta2 theta2_prime];

[t,y]=ode45(@pend, [0 ,tspan],[ 2.5 0 1 0]); %This gives the time vs y vectors

%---position of mass 1 and mass 2----------------------------------------

x1=l1*sin(y(:,1)); %This would give the x coordinates of the mass 1

y1=-l1*cos(y(:,1)); %This would give the y coordinates of the mass 1

x2=l1*sin(y(:,1))+l2*sin(y(:,3));  %This would give the x coordinates of the mass 2

y2=-l1*cos(y(:,1))-l2*cos(y(:,3));  %This would give the y coordinates of the mass 2

%------visualizing the result---------------------------------------------

figure(1)

plot(x1,y1,'linewidth',2) %This would plot out the entire motion of mass 1. The linewidth would be 2.

hold on

plot(x2,y2,'r','linewidth',2) %This would plot out the entire motion of mass 2. The linewidth would be 2.

h=gca; %This would get the current axis handles. If there is no axis, then matlab makes axis and returns it

get(h,'fontSize')

set(h,'fontSize',14) %This is the fontsize of the various markings on the handle

xlabel('X','fontSize',14); %Labels the x-axis

ylabel('Y','fontSize',14); %Labels the y-axis

title('Chaotic Double Pendulum','fontsize',14) %The title of the graph is set here

fh = figure(1);

set(fh, 'color', 'white'); %These two expressions would set and show the above figure.

figure(2)

plot(y(:,1),'linewidth',2) %This would plot the 1st column of y matrix with linewidth 2

hold on

plot(y(:,3),'r','linewidth',2) %This would plot the 3rd column of y matrix with linewidth 2

h=gca;

get(h,'fontSize')

set(h,'fontSize',14)

legend('\theta_1','\theta_2') %This would show the legend showing which lines is theta_1 and theta_2

xlabel('time','fontSize',14);

ylabel('theta','fontSize',14);

title('\theta_1(t=0)=2.5 and \theta_2(t=0)=1.0','fontsize',14)

fh = figure(2);

set(fh, 'color', 'white');

%----movie of double pendulum--------------------------------------

figure(3)

Ncount=0;

fram=0; %Initial counts are intialized

for i=1:length(y)

Ncount=Ncount+1; %After each point, the count is increased

fram=fram+1; %This indicates the frame number.

plot(0, 0,'.','markersize',20); %The initial point is marked with an '.'

hold on %The code in between hold on and hold off would stay on.

plot(x1(i),y1(i),'.','markersize',20); %Plots the postions of 1st mass over time.

plot(x2(i),y2(i),'.','markersize',20); %Plots the positions of 2nd mass over time.

hold off

line([0 x1(i)], [0 y1(i)],'Linewidth',2); %A line will be made with x points as 0 to x1(i) and y points as 0 to y1(i).

axis([-(l1+l2) l1+l2 -(l1+l2) l1+l2]); %Sets the limits for x and y axis to be shown on screen

line([x1(i) x2(i)], [y1(i) y2(i)],'linewidth',2);

h=gca;

get(h,'fontSize')

set(h,'fontSize',12)

xlabel('X','fontSize',12);

ylabel('Y','fontSize',12);

title('Chaotic Motion','fontsize',14)

fh = figure(3);

set(fh, 'color', 'white');

F=getframe;

end

movie(F,fram,20) %This would show the various frames on the screen for a set interval and it would give an illusion of a movie as the frames would be shown on the screen very fast

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

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