fixed issue with heading error derivative

notebook/diff_eq.ipynb

@@ -0,0 +1,102 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & - v \\sin{\\left(\\theta \\right)} & 0 & 0\\\\0 & 0 & v \\cos{\\left(\\theta \\right)} & 0 & 0\\\\0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & - v \\cos{\\left(\\psi \\right)} & 0\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[0, 0, -v*sin(theta),           0, 0],\n",
+       "[0, 0,  v*cos(theta),           0, 0],\n",
+       "[0, 0,             0,           0, 0],\n",
+       "[0, 0,             0,           0, 0],\n",
+       "[0, 0,             0, -v*cos(psi), 0]])"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import sympy as sp\n",
+    "\n",
+    "x,y,theta,psi,cte,v,w = sp.symbols(\"x y theta psi cte v w\")\n",
+    "\n",
+    "gs = sp.Matrix([[ sp.cos(theta)*v],\n",
+    "             [ sp.sin(theta)*v],\n",
+    "             [w],\n",
+    "             [w],\n",
+    "             [ v*sp.sin(-psi)]])\n",
+    "\n",
+    "state = sp.Matrix([x,y,theta,psi,cte])\n",
+    "\n",
+    "gs.jacobian(state)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & 0\\\\\\sin{\\left(\\theta \\right)} & 0\\\\0 & 1\\\\0 & 1\\\\- \\sin{\\left(\\psi \\right)} & 0\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[cos(theta), 0],\n",
+       "[sin(theta), 0],\n",
+       "[         0, 1],\n",
+       "[         0, 1],\n",
+       "[ -sin(psi), 0]])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "state = sp.Matrix([v,w])\n",
+    "\n",
+    "gs.jacobian(state)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.6.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}