added kinematic plotting of Ginsberg p1-10

README.md

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+# ME5180 - Dynamics
+
+## Examples of Numerical Analysis in Dynamics
+
+### 1- Double Pendulum Kinematics
+
+[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. 
+
+

double_pendulum.m

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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
+
+
+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')
+
+% 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")