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added kinematic plotting of Ginsberg p1-10
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# ME5180 - Dynamics | ||
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## Examples of Numerical Analysis in Dynamics | ||
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### 1- Double Pendulum Kinematics | ||
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[double_pendulum.m](./double_pendulum.m) has a script to plot the velocity over time and | ||
create an animation of the link positions. [double_pendulum.ipynb](double_pendulum.ipynb) | ||
shows the output of the code. | ||
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clear all; close all | ||
t=linspace(0,2*pi/50,100); % create time varying from 0-0.126 s (or one period) | ||
x=20*sin(50*t);dx=20*50*cos(50*t); % define x and dx/dt in terms of time (note dx=dx/dt) | ||
t1=0.2*pi*cos(50*t); dt1=-10*pi*sin(50*t); % define theta1 (t1) and dtheta1/dt | ||
t2=0.2*pi*sin(50*t-pi/3); dt2=10*pi*sin(50*t-pi/3); % define theta2 (t2) and dtheta2/dt; | ||
L1=1;L2=1.5; % set lengths for L1 and L2 (none were given in problem so 1 and 1.5 mm were | ||
% chosen arbitrarily | ||
rcc=[x+L1*sin(t1);-L1*cos(t1)]; % position of connection between links | ||
rco=[x+L1*sin(t1)+L2*sin(t2);-(L1*cos(t1)+L2*cos(t2))]; % create a row vectors of | ||
% x-component and y-component of | ||
% pendulum position C (r_C/O) | ||
vco=[dx+L1*cos(t1).*dt1+L2*cos(t2).*dt2;(L1*sin(t1).*dt1+L2*sin(t2).*dt2)]; % create row | ||
% vectors of | ||
% the x- and | ||
% y-component | ||
% velocity of | ||
% point C | ||
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figure(1) | ||
plot(t,vco(1,:),t,vco(2,:)) | ||
xlabel('time (s)') | ||
ylabel('velocity (mm/s)') | ||
legend('x-component','y-component') | ||
title('Velocity of end point') | ||
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% Now plot the position each time step | ||
for i =1:length(t) | ||
hold on | ||
plot([x(i),rcc(1,i),rco(1,i)],[0,rcc(2,i),rco(2,i)]) % plot lines for 2 links | ||
plot(rco(1,:),rco(2,:),'--','LineWidth',2); % this plots all of the positions in the x-y-plane | ||
% over time | ||
plot(rco(1,i),rco(2,i),'o','MarkerSize',10); % this plots the position as a circle at | ||
% timestep i | ||
axis([-30 30 -5 0]) % this sets the axis bounds | ||
filename=sprintf('pendulum_output/%05d.png',i); | ||
print(filename); % another option for saving a plot to a png is the 'print' command | ||
hold off | ||
clf % this clears the figure for the next time step | ||
end | ||
% this is a system command to use ImageMagick's cli 'convert' to create an animated gif | ||
% if you don't have ImageMagick installed, comment this next line | ||
system ("convert -delay 10 -loop 0 pendulum_output/*png pendulum.gif") |
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