DOC: render rotation matrix explicitly (#180)

Co-authored-by: Mikhail Mikhasenko <[email protected]>

docs/appendix.md

@@ -3,6 +3,7 @@
 ```{toctree}
 appendix/dynamics
 appendix/angles
+appendix/rotation-matrix
 appendix/phase-space
 appendix/alignment
 appendix/benchmark

docs/appendix/rotation-matrix.ipynb

@@ -0,0 +1,83 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Explicit rotation matrix"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "```{autolink-concat}\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import sympy as sp\n",
+    "\n",
+    "\n",
+    "def Rz(α):\n",
+    "    return sp.Matrix(\n",
+    "        [\n",
+    "            [sp.cos(α), -sp.sin(α), 0],\n",
+    "            [sp.sin(α), sp.cos(α), 0],\n",
+    "            [0, 0, 1],\n",
+    "        ]\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "def Ry(α):\n",
+    "    return sp.Matrix(\n",
+    "        [\n",
+    "            [sp.cos(α), 0, sp.sin(α)],\n",
+    "            [0, 1, 0],\n",
+    "            [-sp.sin(α), 0, sp.cos(α)],\n",
+    "        ]\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "θ, ϕ, χ = sp.symbols(\"theta phi chi\")\n",
+    "R = Rz(ϕ) @ Ry(θ) @ Rz(χ)\n",
+    "R"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.13"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "d54b55e42db0e71aa222cee01fa24af6ccae1fbbd4d24a4dc92ca39f5243715f"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}