{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "15c6a3e2-8074-4e8e-81b4-580c83aae432",
   "metadata": {},
   "source": [
    "Example 4.3. Astronauts in training are required to practice a docking\n",
    "maneuver under manual control. As a part of this maneuver, it is required to bring\n",
    "an orbiting spacecraft to rest relative to another orbiting craft. The hand\n",
    "controls provide for variable acceleration and deceleration, and there is a device on\n",
    "board that measures the rate of closing between the two vehicles. The following\n",
    "strategy has been proposed for bringing the craft to rest. First, look at the\n",
    "closing velocity. If it is zero, we are done. Otherwise, remember the closing\n",
    "velocity and look at the acceleration control. Move the acceleration control so\n",
    "that it is opposite to the closing velocity (i.e., if closing velocity is positive, we\n",
    "slow down, and we speed up if it is negative) and proportional in magnitude\n",
    "(i.e., we brake twice as hard if we ﬁnd ourselves closing twice as fast). After a\n",
    "time, look at the closing velocity again and repeat the procedure. Under what\n",
    "circumstances will this strategy be eﬀective?    "
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "00596c39-fd28-4204-a856-013b36e954c3",
   "metadata": {},
   "source": [
    "![image.png](attachment:cc7a060a-3209-4edb-936f-89be27180226.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92a2ac8b-d639-4cba-aca0-b268fb81ba24",
   "metadata": {},
   "source": [
    "In Lecture 21 we arrive at the dynamical system\n",
    "$$\n",
    "    X_{n+1}=A X_n\n",
    "    \\quad\\hbox{where}\\quad\n",
    "    A=\\left[\\matrix{\n",
    "        1-w\\kappa & -c\\kappa\\cr\n",
    "        1 & 0\n",
    "    }\\right]\n",
    "    \\quad\\hbox{and}\\quad\n",
    "    X_n=\\left[\\matrix{v_n\\cr v_{n-1}}\\right].\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6ddf573d-2ebb-4310-92a6-a307fa98ba6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Symbolics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c2999925-9870-470f-8931-c42f68b1f855",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Num}:\n",
       "     c\n",
       "     w\n",
       " kappa"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@variables c,w,kappa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d552ba34-b5c5-473e-8cbd-b63439f2afb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Num}:\n",
       " \u001b[96m1\u001b[39m - kappa*w  -c*kappa\n",
       "           1         0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=[1-w*kappa -c*kappa; 1 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3e2c15be-8e43-4b1b-bbee-149846830390",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fA (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a function of kappa returning the matrix A\n",
    "fAs=\"fA(kappa)=\"*string(Symbolics.toexpr(A))\n",
    "eval(Meta.parse(fAs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02b35f1f-ea60-4c3a-8793-fb3f6f337e33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Num}:\n",
       " \u001b[96m1\u001b[39m - kappa*w  -c*kappa\n",
       "           1         0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fA(kappa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c712d2f6-df75-421a-ad23-02752ee006f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Num}:\n",
       " \u001b[96m1\u001b[39m - \u001b[96m10\u001b[39mkappa  \u001b[96m-5\u001b[39mkappa\n",
       "           1        0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fix c and w so the effects of kappa can be explored\n",
    "c=5\n",
    "w=10\n",
    "fA(kappa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e244510c-6107-401f-abf0-21e418803fcf",
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "27d3b985-8ca0-4a9c-9067-2373f91ba4f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 0.1550510257216822\n",
       " 0.6449489742783179"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvals(fA(0.02))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5702a48-d1c0-427e-8e82-edbacec60117",
   "metadata": {},
   "source": [
    "For small positive values of $\\kappa$ the\n",
    "eigenvalues are both positive and less than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1c0c29cd-0791-4bb5-8c27-86be5ef389cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{ComplexF64}:\n",
       " 0.35 - 0.16583123951777004im\n",
       " 0.35 + 0.16583123951777004im"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvals(fA(0.03))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "68e0131c-8c85-400a-9368-d6b0d8d7d026",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 0.3872983346207417\n",
       " 0.3872983346207417"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs.(eigvals(fA(0.03)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "633c7c49-93f2-448b-9042-eb7d3fce9574",
   "metadata": {},
   "source": [
    "When $\\kappa$ is a little larger the eigenvalues\n",
    "are complex and have equal magnitudes which are\n",
    "still less than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8a3974e2-51e6-489b-b7e0-ba3802497236",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{ComplexF64}:\n",
       " -1.0 - 0.7071067811865475im\n",
       " -1.0 + 0.7071067811865475im"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvals(fA(0.3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81e3143d-9362-48ec-ade5-4c7d4d20fc8c",
   "metadata": {},
   "source": [
    "When $\\kappa$ is a bit greater still the eigenvalues are\n",
    "complex but have magnitudes greater than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "45b72ba6-ea79-4127-bf31-79fdb901ccdb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " -3.2247448713915894\n",
       " -0.7752551286084108"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvals(fA(0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "701ba0ad-9a23-4b2e-9a02-46439e6050a5",
   "metadata": {},
   "source": [
    "Whe $\\kappa$ is much larger the eigenvalues are negative\n",
    "and one of them has a magnitude much greater than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9ad86552-761f-42d8-8177-2a77204637d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fabseig2 (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create functions to plot the magnitude of the eigenvalues\n",
    "fabseig1(kappa)=abs(eigvals(fA(kappa))[1])\n",
    "fabseig2(kappa)=abs(eigvals(fA(kappa))[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "23b0da51-f049-4a8e-b8a5-a1f6e6ddcb4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.2247448713915894"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fabseig1(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e78c4de1-df03-4ee0-8fa5-c8afab5df895",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7752551286084108"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fabseig2(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d71b9926-132a-44b1-abec-8f636d5c606b",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "cf334246-881a-454f-9fff-96cc6b953ea4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YJjExsXMXnGZlGYZhamtrO9+Hs7Ky+vTTT7tPqFcoFF0GBD388MOa9eS6rCxz+fLlIUOGdPm19fT01KxUfkeaCYWk0/RBrQkTJnT5m0AkEr333nu3P2DnlWU6q66u1vydER0d3dbWlpWV1Tn2KIrauHHjxx9/TAj55JNPtO/SzCOMj4/v/LeCra3tgQMHOh9cM4/wyJEjnVdx4/F4W7du7bxbQUGBZg6o1rp167744gtCyL/+9a/eXC6wTBSDJ9QDSyorK9vb2z09PbsMaemspKSEpmlfX9/Ow/qLioquX7/e1NTk7+8/adIkPp9fUlLCMEz3v/3lcnlVVZWzs7NYLKZp2t7ens/n19fXawJApVKVlpaKRKIuIzUaGxsbGxtdXFy0664VFRWp1erAwMAux1coFFVVVSqVyt7e3tHRUbNRrVZfvHgxNzfX1tZ26tSp7u7u9fX1zc3N7u7uXVquGRkZiYmJXC53+PDh4eHhLS0tdXV1jo6OXdrEDMOkpqampKS0tbW5ubn5+fkNGzasl+3apqYmTQesj48Pj9d1cFx1dXVSUlJ1dbVarfbx8RkxYsRtmuMadXV1LS0tTk5OXdZNJYRIpdKamhpCiJubm1gsVigUly5dKiwstLa2njBhgo+PT3Nzc319fef3Dh8+PCkpqb6+3tbW9sKFC4WFhfb29tHR0dqLqbFy5crvv/8+Li5u/PjxV65cyczMFAgEkydP7tKGJoQolcr4+Pj8/HyBQDB+/Hh/f//W1tba2truVxVAC0EIluKHH3549NFHFy1adPjwYbZrgb9og7BL8nWhDcIJEyYYrDawHJg+Aebp5Zdftre3nzJlipeXV0VFRUxMzHvvvcfj8bpPTgcAC4cgBPNUU1PzwQcfdN7i5ub25Zdfdn58AQAAQRCCudq7d+/LL7+ckpJSV1fH4/GCg4PHjx+vXV0MjMQzzzxTXV3d03J6WkuWLBk8eDDGf4Ke4B4hAABYNMwjBAAAi4YgBAAAi4YgBAAAi4YgBAAAi4YgBAAAi4YgBAAAi8Z+EL7zzju9fziOZoFUvdZjfvT3pHUzhovWB7hodwsfaH2gj//N2J9HKBaLa2tr7zijVkMul3M4HO2zyKE3WltbtYtHQy/hovWBVCrVPqQeekOhUDAMIxAI2C7ElEilUrFYfO8PU+uM/RYhAAAAixCEAABg0RCEAABg0RCEAABg0RCEAABg0RCEAABg0RCEAABg0RCEAABgMi5Uc5oU/XxMBCEAAJiG/fnq9Yn8NlU/rwPD69/DGczTTz+dmJjIdhX6wuVyf/vtN09PT7YLAQAwFoeK1C9fVR+drPDs3UpkvWeqQXjlypV//OMfoaGhbBeiFw8//HBNTQ2CEABA42iJ+tl4+vRsXoBV/y8LaqpBSAgZOHBgZGQk21XoRS9XXgUAsASnypi1l+gTM3lDHCmptP+Pb8JBCAAAZu98BfPYRdXv0bzhzv250HZnGCwDAABG6koNs/xP1U9TeWNc9ZWCBEEIAADG6Wot80CMav9k3mQPPaYgQRACAIARSq5n5p9R7bmPN91LvylIEIQAAGBsMhqZOadVn4/nzvHWewoSBGE/amxsZJi7HterUCik+hgFBQBgmnKbmZmn6O2juYv8DJRQCMJ+Ex4eXlNTQwipr6/38PC47777mpqatF9VKBTff//9c889t2TJksrKSu32w4cPP/XUUyyUCwBgfIpameg/6HeGc5YHGi6eEIT9z8nJqby83MrK6ptvvtFulEqlP//8s0QiOXToEJqAAADdlcmY6SfpV4ZyHg8xaDYhCPWCw+GsW7du37592i2Ojo7Hjh17/fXXWawKAMBo1XaQmX/Q6wZynhpo6GBCEOpLYmJienr6jRs32C4EAMDYNSnIzD9UywI5Lw9hIZXMZ2WZ5xPooyX9vwZdT7ZEclb13Hhvbm7+5ptvZsyYsXfv3uHDhxusKgAAk9OsINEnVTMHUFsi2WmbmU8Qvh7JfWaw4YLQXXS7Qb1ffvnlpEmT3njjjejo6A8//FAgEBisMAAAEyJTkbmnVePcqH+N5LJVg36DUKlU8vl8vZ5Cy0FAHASGmHFyR0qlcufOnQcPHoyKivL29j5+/PiDDz7IdlEAAEZHoSYPnVUFS6iPx7CWgkR/9wgXLFggFovt7e0HDBjw1Vdf6eksxumHH37w9/cfP348IWTVqlWdh8wAAICGQk0WxagcBdTuiVwOq60YfQXh5s2b6+vrZTLZwYMHN27cmJ6erqcTGRuGYbZv375p0ybNy0cfffTcuXNVVVWEEBcXFx6PRwgJCQmhKKqlpYXNQgEA2EMz5JE/aT6H2jeJ5RQk+usaHT16tOYfEyZMcHFxqaioCA8P19O5jApFUZ1T38nJSSaTaf5dW1vLUlEAAEaEIWT9JbpRwRybweMZwdwFPd4jTEhIyMvLO3v2bERExJQpU26zZ1NTk1wu1/xbJBIJhUL9VQUAAOx6MYHObGLOzOYJ2bwz+D96DMK0tLRLly5du3Zt2rRpt9mto6Nj8ODB2pcLFizYuXNnTzvL5XIOh8Pn89VqdX/W2h9GjBhhZWV1t+9ycXEJDg7uspFhmLa2tv5agEYmk1EU210PpgYXrQ+0nR/QSwqFgmEYpVLJdiEGtSWZG1fDOTZVxXR09OEzTiaTMQzT+19PoVCouSd1G3oMwjVr1qxZs0Yul0dGRu7fv3/VqlU6dxMKheXl5dbW1r05Jp/P1wQhh2MEzem/++KLLyQSCSGEYRiZTGZjY9Obd40bNy4yMrLLRoqirK2te3mEO2IYpr8OZTlw0foGF+2uaILQoqZXvXNTfa5G/edcntM9fNdisbh//07Ve5wIBIKQkJCKigp9n4h1I0eO1NwFbGhoCAkJGTlyZH19vfarmZmZ69evHzVq1JgxY7Zs2dLW1qbZ/vvvvz/33HPsVAwAYECfpKt/yFfHzOY5GVn06yUIq6qq9uzZk5eXV15evnv37rNnz86ePVsfJzJOTk5OFRUVzs7OX3/9tXbj9evX/fz8Pv/88x07dpw6deqFF15gsUIAAAPbnaPekaE+O4frJmK7lG700jXK4/FOnTq1bds2uVweGhp65MiR7r1/Zu/JJ5/85z//+corr2herly5UvulzZs3v/TSSyzVBQBgaAcL1G8kqS/M5XqLjfHWu16C0NnZ+aefftLHkU1IbGxsdnZ2YmKidiaJ1vXr18PCwlipCgDAwI6XMs8n0DFzeEF2xpiCxJzWGm369YuOjKsGO53t9CXisT329zY0NOzdu/f+++/fu3dvlyC8cuXKzp074+Pj9V8jAADL/qxknohTHZ/BC3cw0hQk5hSEdnNW2kx6wFBno7j2zrf58ueffx4dHf3mm29OmDDho48+Eon+6hRPTk5euHDhgQMHOs8YAQAwS4k1zLLzqkPTeCNdjDcFiTkFIUco5gjFbFdBCCFyufw///nPb7/9Fh4eHhgYePTo0aVLlxJC0tPT58yZ8/nnn8+dO5ftGgEA9CutgVkQo9p7H+8+d6NOQYIH8+rDvn37Bg0aNGbMGELI448/rll0Oysra/r06a+//vqUKVMaGxubmprYLhMAQF/ympnZp+nPxnFnext7ChIEYb9jGGbPnj3aRbcffvjh5OTkmpqaX375RaFQbN68OTAwMDAwEF2jAGCuymXMzFP0G5Gcxf6mETHm0zVqJCiKunLlivalo6OjZjGBLVu2bNmyhb26AAAMoa6DRP9BbxjEWRNmGilI0CIEAID+0qwgM0+plgRQ/4gwpXAxpVqN3MSJE/uwZqC7u7uFPKAKAMxbm4rMO6Oa6E69GWUcD5XoNXSN9puDBw/24V1Tpky5/TOqAACMn1JNFp9T+dtSH48xsRQkaBECAMA9UjPk0Qu0gEvtnsg1gUGi3aBFCAAAfccQsuEyXdfBnJhpFI+b7wMEIQAA9N2r1+jkBubsbJ7A9PpE/4IgBACAPno/RX28lIm9n2fDZ7uUe2CqQSgSiSZPnszlmuxfILfV2tqqXZ4UAMA4fZOj3pWtjpvHdTSyB+3eLVMNwnPnzrW3t7Ndhb5wOByJRMJ2FQAAPfqlSP1mkvrCXK6ntSmOj/kbUw1CoVAoFArZrgIAwBKdLWf+L54+Pdt4HzF4V0w1CAEAgBXXapkVF1S/TOMNdTSHFCSYRwgAAL2X18wsPEt/ex9votE/XKn3EIQAANArpVJm+h/0+yM5c03h4Uq9hyAEAIA7q+sgM/6gX4zgrAgyt+Awt+8HAAD6XZuKzD+jWhpAPTvYDFPDDL8lAADoR3KaLIhRDXWi3hpunlO3EYQAANAjzYLa9lbUznHmmYIE0ycAAOA2/i+erpczJ2fyTPK5Er2DIAQAAN3eSlIn1jJ/zjXhBbV7A0EIAAA6fJGl3l+gvnQ/z86UF9TuDQQhAAB09UuRemuyOvZ+rqsFrP+PIAQAgL+5UMk8HU+fmc0LsDXfG4OdYNQoAAD8T1oDs/S8av9k81lK9I4QhAAA8JeiVmb2afo/47jTvSwlBQmCEAAANGo7yKxT9OahnIf8LSsaLOu7BQAAnWQqcv9p1ZIAasMgi8sFi/uGAQCgC5WaLDmnCneg3jbTRdRuD0EIAGDRGELWXqI5FPlqghmvHnM7mD4BAGDRtlynM5uY83N4PEttGSEIAQAs165s9cFCJn4ez9qC08CCv3UAAMv2e4n6rSR13DyLWD7mNhCEAACW6EoNs/YSfXKmpSwfcxuW2iUMAGDBClqYh87S+ybxhjtbegoSBCEAgKWpbiczT9HvjODMGoAUJARBCABgUTQT5x8N4qwOwef/X3AhAAAsBc2QpedUQ52oN6Lw4f8/uBYAAJbiuSs0zZAvx1vi8jG3gVGjAAAW4d8p6svVzMX7LXfifE8QhAAA5u/HAvVX2er4eTxbPtulGB8EIQCAmbtYyTyXQJ+fw/OwZrsUo4QWMgCAOctuYpaeVx2YwhvsgMkSuiEIAQDMVl0HmR9DvzWcO80TKdgjBCEAgHlqV5F5Z1TLAqh1Yfiovx1cHQAAM6RmyGMX6UA76i2LfNbuXcFgGQAAM7T5Ol3dzpyZzUOX6B0hCAEAzM3uHPVvxcyV+TwBWoO9gCAEADAr5yqYf16nY+/nOQrYLsVEIAgBAMxHVhOz4k/VoWm8YAn6RHsLg2UAAMxEbQe5/zT9wWjuRHek4F1AEAIAmAM5TRbGqJYHUo8G4YP97uB6AQCYPIaQNXG0pzX1zggMj7lruEcIAGDy/pWszmlmLszFZIm+QBACAJi2X4vVX2WrE+bzRPhE7xNcNgAAE5ZUxzx1mT41C0+W6DvcIwQAMFWVbeSBGPrL8dxIJ/SJ9h2CEADAJHXQ5IEY1dowzkI/fJLfE1w+AACT9GQcHWBHvRaJj/F7hXuEAACm5/0UdW4zcxHDRPsDghAAwMScuMXszFQnzOdimGi/wFUEADAlWU3M6ljV0Wielxitwf6BzmUAAJPRKCcLYugPRnFHuyIF+w2CEADANNAMWf6naq43tTIYH939CVcTAMA0bL5Gq9Tkg1FYTbSf4R4hAIAJ+KlQ/UsRc/UBHg/tl/6GIAQAMHYpDcwz8fTZOTwnPHReD/CnBQCAUWuQk0Ux9GfjuEMcMUBGLxCEAADGi2bI8vOqRX7U0gB8XOsLriwAgPH653VaTci/MUBGn3CPEADASP1WrP6xgLn+AI+LPlF9QhACABijnGZm/WX6xEyes5DtUswdukYBAIyOTEUePEtvHcEd4YzGoN4hCAEAjM7aOHq0C/VkKD6iDQFdowAAxmVnpjqriYmfj89nA8GFBgAwIldrmXdu0vHzeEIMFDUUtLsBAIxFg5wsOUfvmsANtMOtQcNBEAIAGAWGkMcuqhb7Uwt88clsULjcAABG4YNUdYOcvDcSXaKG1uM9QqVSeerUqYyMjJaWlvfee48Qkp2dbW1t7ePjY8DyAAAswuVq5uM0+uoDPD6aJwanOwjLy8tnzZqVnp4uFAqdnJw0QfjNNy/F1gMAACAASURBVN/Ex8fHx8cbtkIAADNXLycr/qS/uY/nLcatQRbo/ttjzZo1crk8KSnpjz/+0G5csmRJYmJic3Nzb4775ptvDho0SCwWh4SE7N69u3+KBQAwOwwhq2Ppxf7UXG+kIDt0BKFUKj1z5syOHTsiIyMp6n8/mKCgILVafevWrV4eev/+/fX19V9++eXGjRvj4uL6p14AAPPyabq6up3BrUEW6egabWlpoWna39+/y3aVSkUIUSgUvTnum2++qfnH1KlTR48eff369YkTJ95TpQAAZie5gbyXQifMx61BNum49i4uLmKxOCEhocv2M2fO8Hi8oKCguzpBXV3dzZs3R40a1fcaAQDMkUxFVsZxPhnD9bdFpyibdLQI+Xz+I4888sorr3h4eAiFQkIITdMnTpx44YUXFi9ebGdn1/ujK5XKRx55ZNGiRePHj+9pn46ODrFYrH35yCOPfPHFFz3tLJfLORwOn8/vfQ0gk8k6d3FDb+Ci9YFMJmO7BBPzzBXOCAdyv5tcKmW7FNMhk8kYhun9r6dQKOTx7rCGGsUwTPetUql0wYIF58+fFwgENE0LhUKpVBoVFXXmzBknJ6denp6m6eXLl3d0dBw+fPg20SUWi2tra62trXtzTARhH7S2ttra2rJdhYnBResDqVRqY2PDdhUm41CR+rVr9JU5aicbAdu1mBKpVCoWi/v371TdOWljYxMTE3PixIkzZ85UV1dLJJJJkyYtXbq09wmkVqsff/zxpqamo0ePIrcAADorkzHPxNNHpjI2+HQ0ArpbhPdu9erVcXFxe/bsEYlEhBB3d3cvLy+de6JFqG9o3PQBLlofoEXYS2qGRP+hivbivDBQxTCMQIAW4V0wXIvw3uXn50skkueee07zcuXKlc8++6yezgUAYEI+Tlcr1eSlIRxayXYpQAjpHIQHDhz4v//7vzu+oaGhoTfHjY2N7XtRAABmKq2B2ZZKJ87ncSlCs10MaPwvCENCQtauXav5N03Te/bsUavVM2fOdHNzq6+vP3v2bGtr65NPPslSnQAAJk+hJisv0u+P5PphvoQx+V8QjhgxYsSIEZp/b9y4cdiwYb/99pv2NolcLn/88cd7v6wMAAB08VYS7WtDrQrB5HnjouMeYUdHx65duy5evNh5sIBAINi2bZuPj09ZWdmAAQMMWCEAgDm4Wst8m6NOXoSxfkZHxx8mjY2NHR0dXG7Xhe+4XC7DMFVVVQYpDADAfHTQZNVF+pOxXDcR26VANzqC0NXV1c3N7e233+68rKharX7zzTeFQmFISIgBywMAMAdvJtGDHaglAegUNUY6uka5XO6OHTtWrFjh7+9///33u7u719XVnT59uqCgYMeOHXe1xBoAAFyrZfblqlMfRKeokdI9j3DZsmVeXl7btm07ceJERUWFq6trRETEJ598MnfuXAPXBwBg0hRq8kQc/fEYrouQ7VKgBz1OqJ84cSIenAQAcI/+naL2s6GWBaJT1Hjpa2UZAADIamJ2ZtBJC/FJa9R0/3heeumllpYWnV/66quv9FkPAICZYAhZd4l+I4o7QIzp80ZNdxDGxsbW1dVpXzY1NTU0NFhbW7u7uxuqMAAA07Y7R91Bk/UD0Slq7HQHYWJiYpctqampK1eufOWVV/RfEgCAyavrIP+8Tp+ezeOiNWj0evunypAhQz755JN169a1tbXptSAAADOw6Sq9Iogz1BExaALuos0eFhbW0tKSk5Ojv2oAAMxAfDVzppx5M6rr+lxgnO4iCE+cOEEI8fDw0FsxAAAmj2bIM1fobaM4tphAbyJ6NWqUpunCwsILFy5MmzYN42UAAG7j62y1NY9g4qAJ6dWoUQ6H4+npuXXrVjxlHgDgNpoU5K0k+vRsHu4NmpDejhoFAIA7ejuJXujHGYIxMiZFd+P92LFj9fX1XTbW19cfOnRI/yUBAJik/Bbm+3w1xsiYHN1BuGbNmu6jQ3Nzc5csWaL/kgAATNKr19QvRHBd8cRBU3MXt3Pb2tqsra31VwoAgOlKrGESa5jnBmOMjOn52z3C3NzclJQUQkhHR8f58+fLy8u1X2pvb9+7d29wcLChCwQAMAWbrtFvRHFEWF7bBP3th3bixIkXXnhB8+8tW7Z02dXV1XXfvn0GqgsAwHScKWeq28mqEDQHTdLfgnD16tULFiwghIwePfqLL76IiorSfgkrbgMA6MQQsuU6/VYUB8uKmqi/BaFEIpFIJISQc+fOBQQE2NjYsFQVAIDJOHmL6aDJQ/5oDpoq3f3ZQ4YMMXAdAAAm6u0k+vVIDgfNQZP1vyD8/ffft2zZsnHjxieeeGLKlCnd5xFqpKamGqo2AABjd6ackanIQj80B03Y/4LQwcEhIiLC1dWVEDJw4MDm5mb2qgIAMA3vJdOvDEVz0LRRDMOwW4FYLK6tre3lDEW5XM7hcPh8LOp+F1pbW21tbdmuwsTgovWBVCq1tIEFV2uZpefpvMU8Xp8ahAqFgmEYgUDQ33WZM6lUKhaLKao///RAcx4AoI+2p6mfD+f0LQXBePQ4+bO5uTk2Nra4uLjLI+k3bdqk/6oAAIxdqZQ5V67+ZiI6qEye7iA8cuTIE0880dDQ0P1LCEIAAELIl1nqlcF4+q450N2k37BhQ2BgYEJCgkwmY/7OwPUBABghOU2+zVU/NRC9ouZAR4uwrq6usrLy4MGDo0ePNnxBAADG70iJeogjFSzBaFFzoOPPGRsbG4FA0L9jcgAAzMnuHPUToWgOmgkdP0ihULh27dovv/wSHaEAAN2VSpnkeuYBXwShmdA9WMbf3//gwYNjxoyZMWNGl4lBGCwDABbuxwLmQX+OAA+iNxe6J9S7u7tXV1frfEO/NxMxoV7fMDe8D3DR+sByJtQP+1X16Tjufe73ev8IE+r7QB8T6nW3CKuqqvrxHAAAZiO3mantIBPcMIrCfKCPGwDgLvxewizwpbC4qDlBEAIA3IXjper7ffDJaVZ0/zjd3d0pXRwcHKKiot555x25XG7gQgEAWNcoJ8n1zBQPtAfNiu57hC+++OK//vUvZ2fnOXPmuLq6VlRU/Pbbb1wud9WqVampqW+88UZqauqhQ4cMXCsAALviqtRj3ShRj4s0g0nS/fPMzMycPXv2d999x+X+NUD4ww8/nDlzJo/HO3LkyJ49e1avXp2dnR0WFmbAUgEAWHapmhnvhn5Rc6PjJ9rW1rZ///6XXnpJm4KEEKFQ+Nxzz3399deEkFWrVtnZ2SUnJxuuTAAAI3C5mhmP8aJmR0cQNjc3K5VKhULRZbtCoairqyOEUBTl6upK07QhCgQAMA5ymqTUM6NcEITmRkcQurm5eXl5vf766zKZTLuxvr7+vffei4qKIoTI5fKysjJPT0/DlQkAwLbUBiZYQtlgPQ+zo+MeIYfD2blz5+LFi319fadOnerk5FRZWXnu3DmGYc6dO0cIuXDhgre396hRowxeLQAAawpbmWA7NAfNkO67vg888EBCQsKsWbOys7MPHz5cWlq6bNmy5ORkzYOZZs6cmZubKxaLDVsqAACbiluJH9bdM0c9jgIePnz4Dz/8YMhSAACMWYmUGeyAFqEZwjhgAIBeKZEyvjYIQjPUY4tQ0ylaVFTU0tLSefvPP/+s/6oAAIwOukbNle4gPHbs2EMPPSQWizkcjpWVFY/HKysrs7a2xgx6ALBYaBGaK91doy+//HJ0dHRFRcW8efNWr15dWlp68+ZNHx+fxx57zMD1AQAYg5p2IuIRW8ydMEc6WoTt7e25ublff/21UCgkhCiVSkLI0KFDv/766xkzZqxevRrjRQHAQtTWNxfmFdXfKmkrL36J40LIw2xXBP1PRxC2traq1WoXFxdCiIODQ0NDg2Z7VFRUW1tbbm5uZGSkQWsEADCIxmZpYX5xbUmJoqpEWFfi0VLMYdRSWx+lk6+Dk+PywhgEoVnSEYQuLi4ikaisrCw0NDQwMPDjjz+Wy+UCgSAxMZEQYm9vb/AiAQD6X1u7Ii+/uLq4uKOixKqu2KW51EYlbbHxUTj6cd18bIaOdgry93RzHEwIIYShVRWvHGJoFcXFsyfMjY6fKEVRkydPPnr06LRp05YvX/7qq6+OGDFi8ODBf/zxx8iRI/38/AxeJADAvVKp6MLi8rLCYmlZMbe2xKmpyFle12w9QG7vS7n5isfPcwr08x3gFkrpHg5DcXlcO0e6sYbnjNUlzY3uP22+/vprzawJR0fH06dPf/DBB9nZ2Q8++ODWrVupHv4vAQAwKmUVtcUFxU2lxUx1sV1DkWdbeaOVY7u9P3H1FUVOcghY6ec3IIjHvfOB/ovr5KGqq0QQmh/dQejl5eXl5aX599ixY3/99VcDlgQAcNeaW9vyc4tqS4oVFYXW9SWercVKii+z81U7+wuCIuz953sG+gVbC+7lFDwXT1VdZX8VDMYDnd0AYHpUKjq/qKy8sEh6q8iqttilqchO1doqHqBwDOC6+9mMmOAaEujsaDe0X0/Kc/JQ1VX06yHBKOgOQrVa/csvvxw9erSkpKS9vb3zl65fv26QwgAA/qemrqkgt7C+uFBdXSypL/JsK2sSOHXYB1BufsKR0Q5B/v4+niEc/d644Tl7KgrT9XoKYIXuIHz++ec//fTTwMDA0NBQDw8PA9cEABZOrlTl5RVXFha1lxcLawrdW4q5apVU4k87+Qn8B0umzvMMvtd+zj7ge/gqygsNfFIwAB1BKJfLv/zyy9dee+2dd97B0BgAMIDKmsbC3ILG4kKmqsihsdC9vbJZ6C538Od4BFhPWugUHODl4TyY7SJ5Ll4Uh6usLOZ7+LFdC/Qn3RPqFQrFokWLkIIAoA8KpSq/4FZ5QWF7WaGwptC9uYhD1DKJP+0cIAyJlAQsGhDsFyQwxtXMhINHdWQkIgjNjI4gdHZ2Hjx4cHJyclRUlOELAgDz09AozcstqCsqVFcW2NUXebXdahK6KuwDKI8A0X0LnUICvDycw9kusjeEA0e2nPnRdvpStguB/qT7HuGePXseeeQRa2vr6OhoJycnA9cEAKauqLSiOLewtbSQV1Po2lhoq2yV2vrTLgFWfoMkU+d5BPsFGfwOX78QhAyjD36srC7lu/mwXQv0G91BGBgYOHDgwOXLl3f/EsMwei4JAEyMXKnKzS0uzc5WVZWK6woHNBfJeNbt9gHEzV80fJpj8Fp/X4+eVmwxLRSXJx4zU3b5hP2ip9iuBfqN7iBcvHhxfHz8Y489FhQUxOcbY089ALCoubUtJzu/tqhQXZ4vqS/0bCtrEXnQ9n5cr2CbqLHOYYFhDnZs16gv4rFzqj/YYDdzBUdstt+jpdERhA0NDefPn9+zZ8+qVasMXg8AGKPKmsaCnPzG4gKqMt+1Id9e2Sy18aWdA618B9pNnecV6h8ktJJKpTY2NmxXqndce2fryPtaz/0smf8k27VA/9ARhFwul6KoiIgIw1cDAEaiqLSyOLegtSSfX1Xg0VzIpxUy+0DGNVAUPk4S8migv3cIV/djvS2BbfTy6m1PicfP5TlhmrU50BGEEolkxowZJ06cGD58uOELAgDDU6uZgqKyktz8ttJ8YU3+gOYCOUfQYR9I3INEY2c5Bgf5eLuxPo3PeHAlTrZTHmw6/IXz2rfZrgX6ge57hE888cQzzzxTU1MzY8YMa2vrzl+aPn26QQoDAD2iaXVuQWlZbl5baYFNTd6AlsIWKzu5QxDlEWQ96UHHgcHuLg5s12jUbKY82HbzYtvVGOtR0WzXAveK0jkK1N3dvbq6Wucb+n3UqFgsrq2t7RK3PZHL5RwOB+N37kpra6utrS3bVZgY87toNK3OySu5lZsnL8sXV+d7S4sarBzqnIKIR7BzQFBIWLCjw73e3rOQe4Rayoqi2s9fdd24nefi1bcjKBQKhmEEApOcScIWqVQqFov7d70X3S3CM2fOKJXKfjwNABgYTatz80tu5eZ1lOSJa/O9pcVNAielYxDHM8hm+Hi3QcEhtr366xN6wvf0l8x+tH7Pu64bP6IEIrbLgb7THYRDhgwxcB0AcI/UaiavsLQ0O6+tJNemJn9Aa1Gj0EnuGMz1CrIdPdFjYHCIDT6s+5l4/FzFrdyG7993Wv064Vju6CFTh+cRApiwguLyoqzctuJc65o875bCRit7uVMQ1yvUdsQEz8HBoUg+/bNf/Ez9rtcbf/7UYelGYhaLBlggBCGAKblVUVOQmddclCOqyhvQnNfGtZY7BnO8QmyGrXAdFBwqsaBbdEaC4vKcVm+p/fK1pl+/sF/0FLLQFCEIAYxaXWNLdnpOQ0EuryLXqzGXENLmEEJ5BovuW+gSHuriJGG7QCCUQOS87t26r/7Z+NMOhyUb0UdqcnSPGjUkjBrVN/MbAGkALF40WZs8OyuvKjeHKc9xrcu1U7SW2ge1e4RK/EMDBwV7e7qyUlVvWNqo0S4YRUf9nncJh+e0clMvx85g1GgfGG7UKAAYjGZiQ2l2jqI0x74mx72tosXGl3YNEYWNsg97JDjQOwy9baaAshI6r3mr8dDOmk9fdFr9Os/Jne2KoLcQhAAsKK+sy8vIaSnMtq7M8m4uaBI6KZ1DeT6htpNm+g4KCuHjF9M0cbgOSzdKY3+v3fG8w7KNwsFj2C4IegW/bwCGIG3ryMzIrcnNoW5leTTk8tSqdscQ4hkqmrbMNSIMg1zMic19C6x8Qhq++7cw56Zk3hMU34rtiuAOcI/Q/OEeYR/c+0VjGCa/sKw4K7u9KFtSneXRVlFm69vqHib2CwscHObvY4aLNVv4PcIu1O3SpkM7FeUFjstftPIL07kP7hH2Ae4RAhi1phZZZlp2XV4WvzzbpyGnnSeSOw/keofZTpjuGx6MDk+LwhHZOK58pT0lrn7PO6Ih4+3mPsYRitkuCnTT12/m+fPnDx8+nJKSMn369DfffFNPZwFgF8MwuQWlxRnZ8qJMp9ps5/aaNkkg8RgoGjvHMfxFD1esW23pREMnCoIjm49/W/3eGru5q8SjojHR0AjpKwiLioo8PT0rKiqKi4v1dAoAVkil7enp2TXZmfzyLN/GbCnPRuE8kOcbZjf9/sCwgFAel+0CwbhwrG0cljyrGDur6dcvpXFH7ec/KQgZxnZR8Df6CsInnniCEPLqq69WVlbq6RQABlN8qyovLaO9MFtSleHRXimz9f+r2Rfx4iA8rgh6wco7xPXZ7e0plxoPfcZ1cJHMeczKbyDbRcFfcNMCQAeVik5OySnPymBKMwfUZRGGUTgP5PoMsh0/xTc8BHf7oC8oSjRsomjIONnVsw3fv89z9hRNeYjnjwces4/93+eOjg4vr/89zWv+/Pk7d+7saWfZ5eOUrNl6xgqDlGYmpFIp2yWYhhZZR056bnNRjrgiy7c5Xyp0VboNsgoZYTX/YW8vl8D/7qboaFd0sFmn0ZLJZKyPQjcNg8dZh41SpsQ1HfqMEoqFE+bzB43Gwmy9JJPJ1Gp170eNCoXCO040YD8IhUJhRkaGSPTXikR2dnZcbo93Wfijoxt2bLSKGINO9ruC6RM9KauozU5JbyvIdKhKd22rUksCuQPCracstgn2C/Uw3sXMjBNFUZg+cRcmzVeMmdmRkSC/dEx+5gebCfeLx8ziiO3YLsvYURRlntMn7O3tezmPkLK2lSx9ruHAdreXP+dY48Md+iInv6QoNV1ZnOFekyFQyRVOAzm+g8Xjp/qHB4f+t8+ztbWV3SLBIlCUYPAYu6hJyrJ8adyxqq2rhQNHicfOFgSGY3CpIekrCJubm+vr65uamlpbWwsLC+3t7R0dHfvlyFbBw6wj72v86VOnx1/rlwOC2aNpdXpmfllGOlWc5l2X2cEVKd0G8wMiJPOXhQT54CHUwDr+gCCH5c9LFqxpu3a26fB/GKXCelS0eMQ0riO6JQxBXyvLfPvtt1u3btW+XLt27aZNm3Tu2YeVZXgUqfnoWdvJi6xHRfdPuWbNMleWkStVqSnZVVnp/NJ0v/qsepFzvUe4dWD4wGERXh7Od3y7ZV60e4SVZe5WTyvLKEpz2q6ebUuO5bv5WEdNFg2biC5TLX2sLGOqS6wpK4tr/7PJ7YXP8BfTHVnOZ3pbuyItNas6M1V0K82nKa/SZkCLR7gkdEh4ZLiTw91dAcu5aP0IQXi3br/EGkOr5NnX225c6Mi6buUTIho6QTRkHMfG3sBFGhsE4d/WGm09/0tH5lWXp99HZ/rtmfdnuqxNnpqcUZudJi5N8W4tumXjJx0Q4RQWMTQy3NamV8+E08m8L5qeIAjvVi/XGmWUio7Mq+0pcR1ZN/gefsKIsaLwMTwXr9u/y1xhrdG/sZ3yYEd6gvTibzaTF7FdCxiUrE2elpJZk5kiLk31lha12foT7yHWMx7xGjY4xBrrF4O5ofhWoqETREMnMCqlPC+5Pe1K7c6XKSuhcNAo4cARgsAIPODiHplwEBKKcljxYs3HzwkHjeK5DmC7GtCv9g5FanJmdWaquDTFu7VQZutPvIeIZz3qNXQQwg8sBMXjCweOFA4cSRhGWV7YkXWt9cyPDRVbrfwHCUKjhCGRfA8/9JD1gQl3jWpILx9vu3bO9dntmI7aE9Pt5VOp6JSUrPL0VGFJil9zbpmNb6v3UJeBQ4ZGhov1HH6me9FYhK7Ru9Uvj2FSd8jkuSnynKSO3JvqdpkgeIggaIggcAjf3ae/6jQq6BrVwWbc3PaUS60XfrWd+hDbtUA/UKuZjKyCkuSb3OKUgIZMqciDeA8TTXrQc3hEyD3c8wMwVxyhWDRknGjIOEII3VQrz0uR56dKzx9Wy9sFAYMEAeFWAYOtBgQRDpaD75HJByGhKIdlz9d89KwoYqzF3j02A/mFZfnJKar8m341qa18idprqHj0LOfhm0LvcrQngCXj2rtYj5xuPXI6IYRuqpMXpCmKMmRXY1T1VVYDgqz8Blr5hVn5hnHt+mdWt9kw+a5RDWnc0fabsS7PfID+8e6Mtpevpq4p9drN9uybnlX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\" />"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot([fabseig1,fabseig2],0:0.001:0.5,\n",
    "    xlabel=\"kappa\",ylabel=\"magnitude\",\n",
    "    title=\"Magnitude vs Kappa\",\n",
    "    label=[\"|λ1|\" \"|λ2|\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4ddb39d-1cfd-42e3-ba2c-4232b7a3df49",
   "metadata": {},
   "source": [
    "Note the $\\kappa$ where $\\max(|\\lambda_1|,|\\lambda_2|)$\n",
    "is minimized happens when the discriminate is zero--just before\n",
    "the eigenvalues turn complex.  Then\n",
    "the eigenvalues remain less than $1$ until about $\\kappa=0.2$.\n",
    "After this at least one of the eigenvalues has magnitude\n",
    "greater than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c0483003-1805-4673-b2b6-e96cb0fac021",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 0.0\n",
       " 1.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The eigenvalues with no control at all\n",
    "eigvals(fA(0.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7913b9ac-e7de-43b5-a7b2-8d5dc584ed2f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.10",
   "language": "julia",
   "name": "julia-1.10"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.10.10"
  }
 },
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