\relax \providecommand\tcolorbox@label[2]{} \@writefile{toc}{\contentsline {section}{\numberline {1}The nonlinear pendulum model}{1}} \@writefile{toc}{\contentsline {section}{\numberline {2}The linear pendulum model}{1}} \@writefile{toc}{\contentsline {section}{\numberline {3}Comparing two pendulum models}{2}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {1}Nonlinear pendulum derivative}{2}} \@writefile{toc}{\contentsline {section}{\numberline {4}The double pendulum model}{4}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {2}double\_pendulum\_deriv.m evaluates the ODE.}{4}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {3}double\_pendulum\_parameters.m returns parameters.}{4}} \@writefile{toc}{\contentsline {section}{\numberline {5}The system energy}{5}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {4}double\_pendulum\_energy.m returns the energy}{5}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {5}Plotting energy + x axis.}{5}} \@writefile{toc}{\contentsline {section}{\numberline {6}Simulate the small perturbation problem with Forward Euler}{5}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {6}Converting angles to positions.}{6}} \@writefile{toc}{\contentsline {section}{\numberline {7}A code to call euler() for the double pendulum}{6}} \@writefile{lol}{\contentsline {lstlisting}{\numberline {7}Solving double pendulum with euler method.}{6}} \@writefile{toc}{\contentsline {section}{\numberline {8}Graphic results for the small perturbation problem}{7}} \@writefile{toc}{\contentsline {section}{\numberline {9}Experiments}{8}} \@writefile{toc}{\contentsline {section}{\numberline {10}HW \# 10}{9}}