add coord notebook to docs

docs/source/notebooks.rst

@@ -4,6 +4,7 @@ Notebooks
 .. toctree::
    :maxdepth: 2
 
+   notebooks/symbolic/coord.ipynb
    notebooks/symbolic/tensor.ipynb
    notebooks/symbolic/material.ipynb
    notebooks/symbolic/elasticity.ipynb

docs/source/notebooks/symbolic/coord.ipynb

@@ -0,0 +1,362 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Symbolic Coord System Notebook"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sympy as sp\n",
+    "\n",
+    "from mechpy.core.symbolic.coord import (\n",
+    "    SymbolicCoordSystem,\n",
+    "    SymbolicCartesianCoordSystem,\n",
+    "    SymbolicCylindricalCoordSystem,\n",
+    "    SymbolicSphericalCoordSystem,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Cartesian Coord System"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SymbolicCartesianCoordSystem(origin=(0, 0, 0), basis=(x, y, z))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "cartesian_system = SymbolicCartesianCoordSystem()\n",
+    "display(cartesian_system)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Cylindrical Coord System"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(r, theta, z))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "cylindrical_system = SymbolicCylindricalCoordSystem()\n",
+    "display(cylindrical_system)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Cartesian/Cylindrical Conversion"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(r, theta, z))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "SymbolicCartesianCoordSystem(origin=(0, 0, 0), basis=(r*cos(theta), r*sin(theta), z))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(r*cos(theta), r*sin(theta), z)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "symbolic_cylindrical_system = SymbolicCylindricalCoordSystem()\n",
+    "display(symbolic_cylindrical_system)\n",
+    "new_coord_system = symbolic_cylindrical_system.to_cartesian()\n",
+    "display(new_coord_system)\n",
+    "display(new_coord_system.basis)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SymbolicCartesianCoordSystem(origin=(0, 0, 0), basis=(x, y, z))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(sqrt(x**2 + y**2), atan2(y, x), z))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(sqrt(x**2 + y**2), atan2(y, x), z)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "symbolic_cartesian_system = SymbolicCartesianCoordSystem()\n",
+    "display(symbolic_cartesian_system)\n",
+    "new_coord_system = symbolic_cartesian_system.to_cylindrical()\n",
+    "display(new_coord_system)\n",
+    "display(new_coord_system.basis)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(5/2, 5*sqrt(3)/2, 2)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "cylindrical_coord = (5, sp.pi/3, 2)\n",
+    "symbolic_cylindrical_system = SymbolicCylindricalCoordSystem()\n",
+    "cartesian_coord = symbolic_cylindrical_system.get_cartesian_coords(cylindrical_coord)\n",
+    "display(cartesian_coord)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(1, pi/2, 1)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "cartesian_coord = (0, 1, 1)\n",
+    "symbolic_cartesian_system = SymbolicCartesianCoordSystem()\n",
+    "cylindrical_coord = symbolic_cartesian_system.get_cylindrical_coord(cartesian_coord)\n",
+    "display(cylindrical_coord)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### using params"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Example 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "SymbolicCylindricalCoordSystem(origin=(0, 0, 0), basis=(r, theta, z))"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(a/2, sqrt(3)*a/2, b)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "symbolic_cylindrical_system = SymbolicCylindricalCoordSystem()\n",
+    "display(symbolic_cylindrical_system)\n",
+    "a, b = sp.symbols(\"a b\", positive=True)\n",
+    "cylindrical_coord = (a, sp.pi/3, b)\n",
+    "cartesian_coord = symbolic_cylindrical_system.get_cartesian_coords(cylindrical_coord)\n",
+    "display(cartesian_coord)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Evaluation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(1.50000000000000, 2.59807621135332, 5.00000000000000)\n"
+     ]
+    }
+   ],
+   "source": [
+    "eval_coord = SymbolicCoordSystem.coord_eval(cartesian_coord, subs={a: 3, b: 5})\n",
+    "print(eval_coord)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Example 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(a, pi/2, b)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "a, b = sp.symbols(\"a b\", positive=True)\n",
+    "cartesian_coord = (0, a, b)\n",
+    "symbolic_cartesian_system = SymbolicCartesianCoordSystem()\n",
+    "cylindrical_coord = symbolic_cartesian_system.get_cylindrical_coord(cartesian_coord)\n",
+    "display(cylindrical_coord)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Evaluation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(3.00000000000000, 1.57079632679490, 5.00000000000000)\n"
+     ]
+    }
+   ],
+   "source": [
+    "eval_coord = SymbolicCoordSystem.coord_eval(cylindrical_coord, subs={a: 3, b: 5})\n",
+    "print(eval_coord)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "venv",
+   "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": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}