\documentclass[main.tex]{subfiles}
\begin{document}
\slide{Pendulum set-up}
{
\twocolumns{0.3}
{\fig{1}{450px-Pendulum_gravity}{Pendulum setup. \credit{wiki:PendMath}}{Experiment Setup}}
{0.5}
{Equation of motion:
\begin{align*}
F &= -mg\sin\theta = ma, \qquad \\
a &= -g \sin\theta \\
a &= \frac{d^2s}{dt^2} = \ell\frac{d^2\theta}{dt^2} =
\ell\epsilon,\\
\frac{d^2\theta}{dt^2} + \frac{g}{\ell} \sin\theta &= 0,\\
\frac{d^2\theta}{dt^2} + \frac{g}{\ell} \theta &= 0 \text{\ \ (small angle approx.)}.
\end{align*}
}}
\subsection{Basic analysis (spreadsheet \& processing \& octave)}
\slide{A spreadsheet approach\\ modification from translational to rotational system}{
\scriptsize
\begin{tabular}{|l|l|l|l|l|}\hline time& $F(t,\theta,\omega)$&$\epsilon(t)$ &$\omega(t)$ calculation&$\theta(t)$ calculation\\ \hline
$t_0$ & $F_0=F(t_0,\theta_0,\omega_0)$& $\epsilon_0=F_0/m $ & $\omega_0$ (initial cond.) & $\theta_0$ (initial cond.)\\ \hline
$t_1=t_0+\Delta t$ & $F_1=F(t_1,\theta_1,\omega_1)$ & $\epsilon_1=F_1/m$ & $\omega_1=\omega_0+\epsilon_1\Delta t$& $\theta_1=\theta_0+\omega_1\Delta t$\\ \hline
$t_2=t_1+\Delta t$ & $F_2=F(t_2,\theta_2,\omega_2)$ & $\epsilon_2=F_2/m$ & $\omega_2=\omega_1+\epsilon_2\Delta t$& $\theta_2=\theta_1+\omega_2\Delta t$\\ \hline
.. &.. &.. & ..& ..\\ \hline
$t_n=t_{n-1}+\Delta t$ & $F_n=F(t_n,\theta_n,\omega_n)$ & $\epsilon_n=F_n/m$ & $\omega_n=\omega_{n-1}+\epsilon_n\Delta t$& $\theta_n=\theta_{n-1}+\omega_n\Delta t$\\ \hline
\end{tabular}
\\~\\
\normalsize
Let's specify and name basic parameters: object mass in a cell J1 named $m$, time advance in a cell J3 named $dt$, length of the pendulum in J4 named $l$, gravitational constant in J2 named $g$, initial angle in a cell E4 and initial velocity in a cell D4, then
\scriptsize
\begin{tabular}{|l|l|l|l|l|l|}\hline row& column A& column B&column C&column D&column E\\ \hline
4&0 & & B4/$m$ & any number & any number \\
& & & & ($\omega_0$ initial cond.) & ($\theta_0$ initial cond.)\\ \hline
5&A4+$dt$&-$m\cdot g\cdot \sin(E4)$ &B5/$m$&D4+C5*$dt$&E4+D5*$dt$\\ \hline
6&A5+$dt$&-$m\cdot g\cdot \sin(E5)$ &B6/$m$&D5+C6*$dt$&E5+D6*$dt$\\ \hline
7..N-1&.. &.. &.. & ..& ..\\ \hline
N&A(N-1)+$dt$&-$m\cdot g\cdot \sin(E(N-1))$ &BN/$m$&D(N-1)+CN*$dt$&E(N-1)+DN*$dt$\\ \hline
\end{tabular}
\href{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Basic/}{\beamergotobutton{\ButtonRef}}
}
\SlideWithFullFigureWithLink{Pendulum basic @ spreadsheet}{examples/Spreadsheets/1D_Pendulum_Basic/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Basic/}
\SlideWithFullFigureWithLink{Pendulum basic @ processing}{examples/Processing/PendulumBasic/Screenshot.png}{https://editor.p5js.org/vojtech.svob/sketches/vTEaAkgs}
\SlideWithFullFigureWithLink{Pendulum basic @ octave (matlab)}{examples/octave/PendulumBasic/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/octave/PendulumBasic/}
\subsection{Pendulum with friction (spreadsheet \& processing)}
\SlideWithFullFigureWithLink{Pendulum with friction}{examples/Spreadsheets/1D_Pendulum_Friction/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Friction/}
\SlideWithFullFigureWithLink{Pendulum with friction @ processing}{examples/Processing/PendulumFriction/Screenshot.png}{https://editor.p5js.org/vojtech.svob/sketches/qHurFykr}
\subsection{Pendulum - phase space (spreadsheet)}
\SlideWithFullFigureWithLink{Pendulum with friction - phase space}{examples/Spreadsheets/1D_Pendulum_Friction_PhaseSpace/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_Friction_PhaseSpace/}
\subsection{Pendulum - energy conservation (spreadsheet)}
\slide{Energy of the Pendulum}{
\centering
\fig{0.5}{07-06.png}{\credit{HokCons}}{label}
}
\SlideWithFullFigureWithLink{Pendulum - energy conservation analysis}{examples/Spreadsheets/1D_Pendulum_EnergyConservation/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_EnergyConservation/}
\subsection{Pendulum - small angle approximation analysis (spreadsheet)}
\SlideWithFullFigureWithLink{Pendulum - small angle approximation analysis}{examples/Spreadsheets/1D_Pendulum_SmallAngleApprox/Screenshot.png}{http://buon.fjfi.cvut.cz:5002/CTU4WP@ELAB/examples/Spreadsheets/1D_Pendulum_SmallAngleApprox/}
\subsection{Two pendulums (processing)}
\SlideWithFullFigureWithLink{Two pendulums}{examples/Processing/TwoPendulums/Screenshot.png}{https://editor.p5js.org/vojtech.svob/sketches/vXqfkyzU}
\end{document}
