mirror of
https://asciireactor.com/otho/phy-4660.git
synced 2024-11-22 16:15:06 +00:00
52 lines
4.4 KiB
TeX
52 lines
4.4 KiB
TeX
|
\relax
|
||
|
|
\providecommand\hyper@newdestlabel[2]{}
|
||
|
|
\abx@aux@sortscheme{nty}
|
||
|
|
\abx@aux@refcontext{nty/global/}
|
||
|
|
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
|
||
|
|
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
|
||
|
|
\global\let\oldcontentsline\contentsline
|
||
|
|
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
|
||
|
|
\global\let\oldnewlabel\newlabel
|
||
|
|
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
|
||
|
|
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
|
||
|
|
\AtEndDocument{\ifx\hyper@anchor\@undefined
|
||
|
|
\let\contentsline\oldcontentsline
|
||
|
|
\let\newlabel\oldnewlabel
|
||
|
|
\fi}
|
||
|
|
\fi}
|
||
|
|
\global\let\hyper@last\relax
|
||
|
|
\gdef\HyperFirstAtBeginDocument#1{#1}
|
||
|
|
\providecommand\HyField@AuxAddToFields[1]{}
|
||
|
|
\providecommand\HyField@AuxAddToCoFields[2]{}
|
||
|
|
\abx@aux@cite{TANGLEDTALEPHASESPACE}
|
||
|
|
\abx@aux@segm{0}{0}{TANGLEDTALEPHASESPACE}
|
||
|
|
\abx@aux@cite{CHAOSAT50}
|
||
|
|
\abx@aux@segm{0}{0}{CHAOSAT50}
|
||
|
|
\abx@aux@cite{CHAOSDYNAMICS}
|
||
|
|
\abx@aux@segm{0}{0}{CHAOSDYNAMICS}
|
||
|
|
\providecommand \oddpage@label [2]{}
|
||
|
|
\@writefile{toc}{\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax }
|
||
|
|
\@writefile{lof}{\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax }
|
||
|
|
\@writefile{lot}{\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax }
|
||
|
|
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {1}Chaos}{1}{section.1}}
|
||
|
|
\newlabel{sec:chaos}{{1}{1}{Chaos}{section.1}{}}
|
||
|
|
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {2}Phase Space and Poincaré Sections}{1}{section.2}}
|
||
|
|
\newlabel{sec:phasespace}{{2}{1}{Phase Space and Poincaré Sections}{section.2}{}}
|
||
|
|
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Computer-generated model of a periodic function in phase space. A pendulum's angular coordinate would correspond to $\theta =x$. The motion is predictable and orbits a single point.\relax }}{2}{figure.caption.1}}
|
||
|
|
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
|
||
|
|
\newlabel{fig:model_periodic}{{1}{2}{Computer-generated model of a periodic function in phase space. A pendulum's angular coordinate would correspond to $\theta =x$. The motion is predictable and orbits a single point.\relax }{figure.caption.1}{}}
|
||
|
|
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {3}Modeling Chaos in a Driven Pendulum}{3}{section.3}}
|
||
|
|
\newlabel{sec:modeling}{{3}{3}{Modeling Chaos in a Driven Pendulum}{section.3}{}}
|
||
|
|
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {4}Chaos compared against Randomsdfness}{3}{section.4}}
|
||
|
|
\newlabel{sec:reverbmap}{{4}{3}{Chaos compared against Randomsdfness}{section.4}{}}
|
||
|
|
\@writefile{toc}{\defcounter {refsection}{0}\relax }\@writefile{toc}{\contentsline {section}{\numberline {5}Discussion}{3}{section.5}}
|
||
|
|
\newlabel{sec:discussion}{{5}{3}{Discussion}{section.5}{}}
|
||
|
|
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Computer-generated model of a driven pendulum with no damping. Arguments: $\theta =x, f=1, I=1, \omega =0.5, \alpha =0, k={\begingroup \omega _0^2\endgroup \over I}=1.5, \phi =0$, 180 time steps.\relax }}{4}{figure.caption.3}}
|
||
|
|
\newlabel{fig:model_no_drag}{{2}{4}{Computer-generated model of a driven pendulum with no damping. Arguments: $\theta =x, f=1, I=1, \omega =0.5, \alpha =0, k=\frac {\omega _0^2}{I}=1.5, \phi =0$, 180 time steps.\relax }{figure.caption.3}{}}
|
||
|
|
\@writefile{lof}{\defcounter {refsection}{0}\relax }\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Computer-generated model of a driven pendulum with no damping. Arguments: $\theta =x, f=1, I=1, \omega =0.5, \alpha =0, k={\begingroup \omega _0^2\endgroup \over I}=1.5, \phi =0$, 180 time steps.\relax }}{5}{figure.caption.4}}
|
||
|
|
\newlabel{fig:chaotic_b_time}{{3}{5}{Computer-generated model of a driven pendulum with no damping. Arguments: $\theta =x, f=1, I=1, \omega =0.5, \alpha =0, k=\frac {\omega _0^2}{I}=1.5, \phi =0$, 180 time steps.\relax }{figure.caption.4}{}}
|
||
|
|
\abx@aux@refcontextdefaultsdone
|
||
|
|
\abx@aux@defaultrefcontext{0}{CHAOSDYNAMICS}{nty/global/}
|
||
|
|
\abx@aux@defaultrefcontext{0}{CHAOSAT50}{nty/global/}
|
||
|
|
\abx@aux@defaultrefcontext{0}{TANGLEDTALEPHASESPACE}{nty/global/}
|