From 61b5ce20f25c5785e41574998a12c6d06eb05a5e Mon Sep 17 00:00:00 2001 From: Thomas Albers Date: Wed, 8 Mar 2023 23:43:00 +0100 Subject: Restructure build system and directory structures --- math/polar_coordinates.org | 36 ------------------------------------ 1 file changed, 36 deletions(-) delete mode 100644 math/polar_coordinates.org (limited to 'math/polar_coordinates.org') diff --git a/math/polar_coordinates.org b/math/polar_coordinates.org deleted file mode 100644 index ff07be3..0000000 --- a/math/polar_coordinates.org +++ /dev/null @@ -1,36 +0,0 @@ -#+TITLE:Polar Coordinates -#+SETUPFILE: ../math_options.org -#+LATEX_HEADER: \usepackage{bm} -#+LATEX_HEADER: \usepackage{mathtools} -#+LATEX_HEADER: \newcommand{\deriv}[2]{\frac{\text{d}#1}{\text{d}#2}} -#+LATEX_HEADER: \newcommand{\unitv}[1]{\bm{\hat{e}}_#1} - -* Disclaimer -This site as of now just a technology demonstration and its claims -should not be taken as true (even though I myself am pretty confident -they are) -* Coordinate transformations -\begin{align*} -x &= r \cos\theta\\ -y &= r \sin\theta -\end{align*} - -* Local unit vectors -\begin{align*} -\unitv{r} &= \cos\theta \unitv{x} + \sin\theta \unitv{y}\\ -\unitv{\theta} &= -\sin\theta \unitv{x} + \cos\theta \unitv{y} -\end{align*} - -* Kinematic in polar coordinates -** Time derivatives of the local unit vectors -\begin{align*} -\deriv{\unitv{r}}{t} &= \dot{\theta}\unitv{\theta}\\ -\deriv{\unitv{\theta}}{t} &= -\dot{\theta}\unitv{r} -\end{align*} -** Position vector and its time derivatives -\begin{align*} -\bm{r} &= r\unitv{r}\\ -\bm{v} &= \dot{r}\unitv{r} + r\dot\theta\unitv{\theta}\\ -\bm{a} &= \left(\ddot{r} - r\dot\theta^2\right)\unitv{r} -+ \left(2\dot{r}\dot\theta + r\ddot\theta\right)\unitv{\theta} -\end{align*} -- cgit v1.2.3