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fixed bib
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@ -110,3 +110,4 @@ url = {http://www.engineeringtoolbox.com/air-density-specific-weight-d_600.html}
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month=oct # "~28",
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month=oct # "~28",
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publisher={Google Patents},
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publisher={Google Patents},
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note={WO Patent App. PCT/GB2004/001,654}
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note={WO Patent App. PCT/GB2004/001,654}
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}
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@ -52,12 +52,13 @@ A 2-dimensional phase space is a useful environment in which to identify the cha
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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
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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
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\begin{figure}
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\begin{figure}
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\hfill
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\includegraphics[width=6.5in]{model_damped_phase.png}
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\subfigure[A]{\includegraphics[width=3in]{model_damped_phase.png}}
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\caption{Model of a damped oscillator in phase space within a single rotation. The critical point is stable. \cite{CHAOSDYNAMICS}}
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\hfill
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\end{figure}
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\subfigure[B]{\includegraphics[width=3in]{model_driven_phase.png}}
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\hfill
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\begin{figure}
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\caption{[A] Model of a damped oscillator in phase space within a single rotation. The critical point is stable. [B] }
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\includegraphics[width=6.5in]{model_driven_phase.png}
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\caption{Model of a damped oscillator in phase space within a single rotation. The critical point is stable.}
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\end{figure}
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\end{figure}
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\subsection{Chaotic Attractor}
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\subsection{Chaotic Attractor}
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