% ____________________________________________________________________ % Nonlinear dynamics I: Chaos % % Supplementary code for Pset 1 % ____________________________________________________________________ % % The first part of the code plots a function y = f(x). % The second part of the code plots a trajectory of a particle, for which % the two coordinates (x,y) are given as a function of time. % % ____________________________________________________________________ % Part I % ____________________________________________________________________ % objective: plot y = sin(x) and y = cos(x) for 0<=x <= pi, % label the graphs, put in title, make lines thicker % clear all; % clears all the values of the variables that you used before close all; % closes all the figure windows that you used before clc; % clears the command window screen % make an array x (from 0 to pi with a step of 0.1) x = 0:0.1:pi ; % open figure 42 (matlab enumerates figures, you can give them different % numbers if you want several plots on different figures figure(42); % plot y = sin(x) in dots in red color plot(x,sin(x),'.r'); % tell the figure to "hold on", otherwise when you plot the next graph it % will erase the previous one hold on; % plot y = cos(x) in dash-dot in blue plot(x,cos(x),'-.b','LineWidth',4); % give anohter variable y the values of sin(x+0.2). It will be an array % since x is an array y = sin(x+0.2); % in 2D plot y = f(x) plot(x,y,'k'); % give labels to the x and y axes, put in a title in bigger font xlabel x ylabel y title('y = sin(x) and y = cos(x)','FontSize',20); % if you don't use axis tight, MATLAB leaves some space on the left and % right of the graph, so the x axis would be from -0.3 to 3.5 % (approximately) instead of 0 to pi. axis tight; % you can label all the graphs that you plotted legend('y = sin(x)','y = cos(x)', 'y = sin(x + 0.2)'); % ____________________________________________________________________ % Part II % ____________________________________________________________________ % objective: plot a trajectory of a particle, for which % the two coordinates (x,y) are given as a function of time. t = 0:0.01:10; x = sin(t); y = cos(t); figure(2); plot(x,y,'m','LineWidth',4); xlabel('x','FontSize',20); ylabel('y'); title('Trajectory of a particle','FontSize',24); axis equal; grid on; % ____________________________________________________________________ % Part III % ____________________________________________________________________ % objective: how to look for help? Type help and then the name of the % function that you want the description of. help plot3