% ____________________________________________________________________
% 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.
%
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% Part I
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% 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
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% objective: how to look for help? Type help and then the name of the
% function that you want the description of.
help plot3