fixed bib

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caes 2017-02-12 22:42:42 -05:00
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@ -110,3 +110,4 @@ url = {http://www.engineeringtoolbox.com/air-density-specific-weight-d_600.html}
month=oct # "~28", month=oct # "~28",
publisher={Google Patents}, publisher={Google Patents},
note={WO Patent App. PCT/GB2004/001,654} note={WO Patent App. PCT/GB2004/001,654}
}

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@ -52,12 +52,13 @@ A 2-dimensional phase space is a useful environment in which to identify the cha
An undriven and undamped oscillator will always return to the same point after one period, so a Poincar\'e map sampled using the period corresponding to the oscillator's natural frequency will consist of a single dot. Figure \ref{fig:models_damped_driven} demonstrates a damped oscillator, which exhibits stable critical points where the velocity goes to zero. A driven oscillator's path orbits around these critical points but can be seen to jump between them in an unpredictable way along the position coordinate An undriven and undamped oscillator will always return to the same point after one period, so a Poincar\'e map sampled using the period corresponding to the oscillator's natural frequency will consist of a single dot. Figure \ref{fig:models_damped_driven} demonstrates a damped oscillator, which exhibits stable critical points where the velocity goes to zero. A driven oscillator's path orbits around these critical points but can be seen to jump between them in an unpredictable way along the position coordinate
\begin{figure} \begin{figure}
\hfill \includegraphics[width=6.5in]{model_damped_phase.png}
\subfigure[A]{\includegraphics[width=3in]{model_damped_phase.png}} \caption{Model of a damped oscillator in phase space within a single rotation. The critical point is stable. \cite{CHAOSDYNAMICS}}
\hfill \end{figure}
\subfigure[B]{\includegraphics[width=3in]{model_driven_phase.png}}
\hfill \begin{figure}
\caption{[A] Model of a damped oscillator in phase space within a single rotation. The critical point is stable. [B] } \includegraphics[width=6.5in]{model_driven_phase.png}
\caption{Model of a damped oscillator in phase space within a single rotation. The critical point is stable.}
\end{figure} \end{figure}
\subsection{Chaotic Attractor} \subsection{Chaotic Attractor}