From 61b5ce20f25c5785e41574998a12c6d06eb05a5e Mon Sep 17 00:00:00 2001
From: Thomas Albers <thomas@thomaslabs.org>
Date: Wed, 8 Mar 2023 23:43:00 +0100
Subject: Restructure build system and directory structures

---
 math/spherical_coordinates.org | 39 ---------------------------------------
 1 file changed, 39 deletions(-)
 delete mode 100644 math/spherical_coordinates.org

(limited to 'math/spherical_coordinates.org')

diff --git a/math/spherical_coordinates.org b/math/spherical_coordinates.org
deleted file mode 100644
index 1c7fd9c..0000000
--- a/math/spherical_coordinates.org
+++ /dev/null
@@ -1,39 +0,0 @@
-#+TITLE:Spherical 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 \sin\theta \cos\varphi\\
-y &= r \sin\theta \sin\varphi\\
-z &= r \cos\theta
-\end{align*}
-
-* Local unit vectors
-\begin{align*}
-\bm{\hat{e}}_r &= \sin\theta \cos\varphi \bm{\hat{e}}_x + \sin\theta \sin\varphi \bm{\hat{e}}_y + \cos\theta \bm{\hat{e}}_z\\
-\bm{\hat{e}}_\theta &= \cos\theta \cos\varphi \bm{\hat{e}}_x + \cos\theta \sin\varphi \bm{\hat{e}}_y - \sin\theta \bm{\hat{e}}_z\\
-\bm{\hat{e}}_\varphi &= - \sin\theta \sin\varphi \bm{\hat{e}}_x + \sin\theta \cos\varphi \bm{\hat{e}}_y
-\end{align*}
-* Kinematic in spherical coordinates
-** Time derivatives of the local unit vectors
-\begin{align*}
-\deriv{\unitv{r}}{t} &= \dot{\theta}\unitv{\theta} + \dot{\varphi}\sin\theta \unitv{\varphi}\\
-\deriv{\unitv{\theta}}{t} &= -\dot{\theta}\unitv{r} + \dot{\varphi}\cos\theta \unitv{\varphi}\\
-\deriv{\unitv{\varphi}}{t} &= -\dot{\varphi} \left(\sin\theta\unitv{r} + \cos\theta\unitv{\theta}\right)
-\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} + r\dot\varphi\sin\theta\unitv{\varphi}\\
-\bm{a} &= \left(\ddot{r} - r\dot\theta^2 - r\dot\varphi^2\sin^2\theta\right)\unitv{r}
-+ \left(2\dot{r}\dot\theta + r\ddot\theta - r\dot\varphi^2\sin\theta\cos\theta\right)\unitv{\theta}
-+ \left(2\dot{r}\dot\varphi\sin\theta + 2r\dot\theta\dot\varphi\cos\theta + r\ddot\varphi\sin\theta\right)\unitv{\varphi}
-\end{align*}
-- 
cgit v1.2.3