{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "de011821",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# Višja dinamika -- Nelinearni sistemi\n",
    "\n",
    "Dr. Janko Slavič, april 2013 (prevod izvirnega Mathematica zvezka v\n",
    "Python).\n",
    "\n",
    "Zvezek obravnava dva zgleda nelinearnih nihajočih sistemov: matematično\n",
    "nihalo (fazna metoda in eksaktna rešitev prek eliptičnega integrala) ter\n",
    "Duffingov oscilator s kubično nelinearnostjo (prosto in vsiljeno nihanje,\n",
    "perturbacijska rešitev po Lindstedt-Poincaréju)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca0975bf",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Fazna metoda -- matematično nihalo\n",
    "\n",
    "Nedušeno nihalo (brezrazsežno, $g/l = 1$) ubogá enačbo\n",
    "\n",
    "$$ \\ddot\\varphi + \\sin\\varphi = 0. $$\n",
    "\n",
    "Ker sistem nima dušenja, je energija ohranjena; z množenjem enačbe z\n",
    "$\\dot\\varphi$ in integracijo dobimo fazno relacijo med kotom $\\varphi$ in\n",
    "kotno hitrostjo $z = \\dot\\varphi$:\n",
    "\n",
    "$$ z^2 = 2\\left(\\cos\\varphi - \\cos\\varphi_0\\right), $$\n",
    "\n",
    "kjer je $\\varphi_0$ zasuk v skrajni legi (amplituda), pri kateri je\n",
    "$\\dot\\varphi = 0$. Vsaka vrednost $\\varphi_0$ določa eno zaprto krivuljo v\n",
    "faznem prostoru $(\\varphi, z)$ -- družino teh krivulj imenujemo fazni\n",
    "portret."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6272211f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:00.216681Z",
     "iopub.status.busy": "2026-09-25T06:49:00.216553Z",
     "iopub.status.idle": "2026-09-25T06:49:00.718539Z",
     "shell.execute_reply": "2026-09-25T06:49:00.718036Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "\n",
    "for phi0 in [0.3, 1.0, 2.0, 2.5, 3.0]:\n",
    "    phi = np.linspace(-phi0, phi0, 400)\n",
    "    z = np.sqrt(2 * (np.cos(phi) - np.cos(phi0)))\n",
    "    ax.plot(phi, z, color=\"tab:blue\", linewidth=1.5)\n",
    "    ax.plot(phi, -z, color=\"tab:blue\", linewidth=1.5)\n",
    "\n",
    "# separatrisa (phi0 = pi, meja med nihanjem in vrtenjem)\n",
    "phi_sep = np.linspace(-np.pi + 1e-3, np.pi - 1e-3, 400)\n",
    "z_sep = np.sqrt(2 * (np.cos(phi_sep) - np.cos(np.pi)))\n",
    "ax.plot(phi_sep, z_sep, color=\"tab:red\", linewidth=1.5, label=r\"separatrisa ($\\varphi_0=\\pi$)\")\n",
    "ax.plot(phi_sep, -z_sep, color=\"tab:red\", linewidth=1.5)\n",
    "\n",
    "ax.set_xlabel(r\"$\\varphi$\")\n",
    "ax.set_ylabel(r\"$z=\\dot\\varphi$\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b68d638a",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Znotraj separatrise (rdeča krivulja) nihalo niha okrog spodnje ravnovesne\n",
    "lege, zunaj nje pa energija zadošča za polni obrat -- gibanje ni več\n",
    "nihanje, temveč vrtenje. Naslednja animacija prikaže, kako se fazna\n",
    "krivulja širi, ko amplituda $\\varphi_0$ narašča proti $\\pi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a76905bf",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:00.719907Z",
     "iopub.status.busy": "2026-09-25T06:49:00.719743Z",
     "iopub.status.idle": "2026-09-25T06:49:03.352978Z",
     "shell.execute_reply": "2026-09-25T06:49:03.352470Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_imgbc1d84d6c0224a76908b1b595d3542b0\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_sliderbc1d84d6c0224a76908b1b595d3542b0\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"animbc1d84d6c0224a76908b1b595d3542b0.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animbc1d84d6c0224a76908b1b595d3542b0.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectbc1d84d6c0224a76908b1b595d3542b0\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_bc1d84d6c0224a76908b1b595d3542b0\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_bc1d84d6c0224a76908b1b595d3542b0\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_bc1d84d6c0224a76908b1b595d3542b0\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_bc1d84d6c0224a76908b1b595d3542b0\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_bc1d84d6c0224a76908b1b595d3542b0\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_bc1d84d6c0224a76908b1b595d3542b0\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgbc1d84d6c0224a76908b1b595d3542b0\";\n",
       "    var slider_id = \"_anim_sliderbc1d84d6c0224a76908b1b595d3542b0\";\n",
       "    var loop_select_id = \"_anim_loop_selectbc1d84d6c0224a76908b1b595d3542b0\";\n",
       "    var frames = new Array(80);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAGQCAYAAAByNR6YAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animbc1d84d6c0224a76908b1b595d3542b0 = new Animation(frames, img_id, slider_id, 40.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import HTML\n",
    "\n",
    "vrednosti_phi0 = np.linspace(0.05, np.pi - 0.02, 80)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 4))\n",
    "ax.set_xlim(-np.pi, np.pi)\n",
    "ax.set_ylim(-3, 3)\n",
    "ax.set_xlabel(r\"$\\varphi$\")\n",
    "ax.set_ylabel(r\"$z=\\dot\\varphi$\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "zgornja, = ax.plot([], [], color=\"tab:blue\", linewidth=1.5)\n",
    "spodnja, = ax.plot([], [], color=\"tab:blue\", linewidth=1.5)\n",
    "\n",
    "\n",
    "def animiraj_fazni_portret(okvir):\n",
    "    \"\"\"Nariše fazno krivuljo nihala za dano amplitudo v okvirju animacije.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    okvir : int\n",
    "        Zaporedna številka okvirja animacije.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    tuple\n",
    "        Posodobljena `Line2D` objekta zgornje in spodnje veje krivulje.\n",
    "    \"\"\"\n",
    "    phi0 = vrednosti_phi0[okvir]\n",
    "    phi = np.linspace(-phi0, phi0, 300)\n",
    "    z = np.sqrt(2 * (np.cos(phi) - np.cos(phi0)))\n",
    "    zgornja.set_data(phi, z)\n",
    "    spodnja.set_data(phi, -z)\n",
    "    return zgornja, spodnja\n",
    "\n",
    "\n",
    "anim = FuncAnimation(fig, animiraj_fazni_portret, frames=len(vrednosti_phi0), interval=40, blit=True)\n",
    "plt.close()\n",
    "HTML(anim.to_jshtml())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "482f37dc",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Eksaktna metoda -- perioda nihala\n",
    "\n",
    "Iz fazne relacije $\\dot\\varphi = \\sqrt{2(\\cos\\varphi-\\cos\\varphi_0)}$ sledi\n",
    "perioda nihanja kot štirikratnik časa, potrebnega za pot od skrajne lege\n",
    "$\\varphi_0$ do ravnovesja:\n",
    "\n",
    "$$ T(\\varphi_0) = 4\\int_0^{\\varphi_0}\n",
    "   \\frac{\\mathrm{d}\\varphi}{\\sqrt{2(\\cos\\varphi-\\cos\\varphi_0)}}. $$\n",
    "\n",
    "Integral ima integrabilno singularnost pri zgornji meji ($\\dot\\varphi\\to0$),\n",
    "zato jo `quad` eksplicitno navedemo prek `points`. Primerjalno perioda ima\n",
    "tudi zaprto obliko s popolnim eliptičnim integralom prve vrste,\n",
    "$T(\\varphi_0) = 4\\,K\\!\\left(\\sin^2(\\varphi_0/2)\\right)$ (za $g/l=1$), ki jo\n",
    "ponuja `scipy.special.ellipk`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a0a509d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:03.365161Z",
     "iopub.status.busy": "2026-09-25T06:49:03.365009Z",
     "iopub.status.idle": "2026-09-25T06:49:03.592471Z",
     "shell.execute_reply": "2026-09-25T06:49:03.591981Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(135°) / T_linearna = 1.5279475882\n",
      "kontrola z ellipk    = 1.5279475882\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from scipy.integrate import quad\n",
    "from scipy.special import ellipk\n",
    "\n",
    "\n",
    "def perioda_nihala_kvad(phi0):\n",
    "    \"\"\"Perioda nihala z amplitudo `phi0` z numerično integracijo (quad).\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    phi0 : float\n",
    "        Amplituda nihanja [rad], $0 < \\\\varphi_0 < \\\\pi$.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float\n",
    "        Perioda nihanja $T(\\\\varphi_0)$ [s] (pri $g/l=1$).\n",
    "    \"\"\"\n",
    "    integrand = lambda phi: 1 / np.sqrt(2 * (np.cos(phi) - np.cos(phi0)))\n",
    "    cetrtina, _ = quad(integrand, 0, phi0, points=[phi0], limit=200)\n",
    "    return 4 * cetrtina\n",
    "\n",
    "\n",
    "def perioda_nihala_ellipk(phi0):\n",
    "    \"\"\"Perioda nihala z amplitudo `phi0` prek popolnega eliptičnega integrala.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    phi0 : float\n",
    "        Amplituda nihanja [rad].\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float\n",
    "        Perioda nihanja $T(\\\\varphi_0)$ [s] (pri $g/l=1$).\n",
    "    \"\"\"\n",
    "    return 4 * ellipk(np.sin(phi0 / 2) ** 2)\n",
    "\n",
    "\n",
    "phi0_test = np.deg2rad(135)\n",
    "razmerje_period = perioda_nihala_kvad(phi0_test) / (2 * np.pi)\n",
    "print(f\"T(135°) / T_linearna = {razmerje_period:.10f}\")\n",
    "print(f\"kontrola z ellipk    = {perioda_nihala_ellipk(phi0_test) / (2 * np.pi):.10f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe6e3507",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Razmerje $T(\\varphi_0)/(2\\pi)$ pove, za koliko je nihanje pri veliki\n",
    "amplitudi počasnejše od linearnega nihala ($T_{\\text{lin}}=2\\pi$): pri\n",
    "$\\varphi_0=135°$ je perioda za dobrih 50 % daljša. Spodaj je ta odvisnost\n",
    "prikazana za celoten fizikalni razpon amplitud."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "74c226d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:03.593619Z",
     "iopub.status.busy": "2026-09-25T06:49:03.593432Z",
     "iopub.status.idle": "2026-09-25T06:49:03.879355Z",
     "shell.execute_reply": "2026-09-25T06:49:03.878880Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "phi0_niz = np.linspace(0.01, np.pi - 0.01, 300)\n",
    "razmerje_niz = np.array([perioda_nihala_kvad(p) for p in phi0_niz]) / (2 * np.pi)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(np.rad2deg(phi0_niz), razmerje_niz, color=\"tab:blue\", linewidth=1.5)\n",
    "ax.axhline(1.0, color=\"black\", linewidth=1, linestyle=\"--\")\n",
    "ax.set_xlabel(r\"amplituda $\\varphi_0$ [°]\")\n",
    "ax.set_ylabel(r\"$T(\\varphi_0)/T_{\\mathrm{lin}}$\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e207fb45",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Duffingov sistem -- kubična nelinearnost\n",
    "\n",
    "Prosto (nevsiljeno) nihanje z blago kubično nelinearnostjo:\n",
    "\n",
    "$$ \\ddot{x} + \\omega_0^2 x + \\varepsilon x^3 = 0, \\qquad\n",
    "   x(0)=A_0,\\ \\dot{x}(0)=0. $$\n",
    "\n",
    "Parametri so isti kot v izvirnem zvezku: $\\omega_0 = 2\\pi\\cdot10$,\n",
    "$\\varepsilon = \\omega_0^2\\sqrt{10}$ in $A_0 = 0{,}5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "212acaa1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:03.880629Z",
     "iopub.status.busy": "2026-09-25T06:49:03.880503Z",
     "iopub.status.idle": "2026-09-25T06:49:04.080906Z",
     "shell.execute_reply": "2026-09-25T06:49:04.080412Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "w0 = 10 * 2 * np.pi\n",
    "eps = w0**2 * 10**0.5\n",
    "A0 = 0.5\n",
    "T = 1.0\n",
    "\n",
    "\n",
    "def enacba_prosti_duffing(t, y):\n",
    "    x, v = y\n",
    "    return [v, -(w0**2) * x - eps * x**3]\n",
    "\n",
    "\n",
    "resitev = solve_ivp(\n",
    "    enacba_prosti_duffing, [0, T], [A0, 0.0], dense_output=True, rtol=1e-10, atol=1e-12\n",
    ")\n",
    "\n",
    "t_niz = np.linspace(0, T, 1001)\n",
    "x_niz = resitev.sol(t_niz)[0]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(t_niz, x_niz, color=\"tab:red\", linewidth=1.5)\n",
    "ax.set_xlabel(\"t [s]\")\n",
    "ax.set_ylabel(\"x [m]\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79333a43",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Frekvenčna vsebina odziva\n",
    "\n",
    "Kubična nelinearnost ustvari harmonike na lihih večkratnikih osnovne\n",
    "frekvence (3., 5., ...); to preverimo s hitro Fourierovo transformacijo\n",
    "(protipomen izvirnega `Fourier`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fbc3794c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:04.082159Z",
     "iopub.status.busy": "2026-09-25T06:49:04.082011Z",
     "iopub.status.idle": "2026-09-25T06:49:04.145591Z",
     "shell.execute_reply": "2026-09-25T06:49:04.145128Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "spekter = np.fft.rfft(x_niz - x_niz.mean())\n",
    "frekvence = np.fft.rfftfreq(len(t_niz), d=t_niz[1] - t_niz[0])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(frekvence[:100], np.abs(spekter[:100]), color=\"tab:red\", linewidth=1.5)\n",
    "ax.set_xlabel(\"f [Hz]\")\n",
    "ax.set_ylabel(r\"$|X(f)|$\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d1814ef",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Lindstedt-Poincaré rešitev\n",
    "\n",
    "Klasična perturbacijska metoda odpravi *sekularne* člene (člene oblike\n",
    "$\\tau\\sin\\tau$, ki v rešitvi naraščajo brez meje), tako da frekvenco\n",
    "razvijemo skupaj z rešitvijo. Uvedemo skalirani čas $\\tau=\\omega t$\n",
    "($\\omega$ je iskana, še neznana frekvenca nelinearnega nihanja) in\n",
    "nastavek\n",
    "\n",
    "$$ x(\\tau) = x_0(\\tau) + \\varepsilon x_1(\\tau) + \\dots, \\qquad\n",
    "   \\omega^2 = \\omega_0^2 + \\varepsilon k_1 + \\dots $$\n",
    "\n",
    "Po vstavitvi v enačbo ($\\omega^2 x'' + \\omega_0^2 x + \\varepsilon x^3=0$,\n",
    "odvodi so zdaj po $\\tau$) in razvrstitvi po redih $\\varepsilon$ dobimo:\n",
    "\n",
    "* red $\\varepsilon^0$: $x_0''+x_0=0 \\Rightarrow x_0=A\\cos\\tau$ (amplituda\n",
    "  $A$ je določena z začetnim pogojem, $A=A_0$);\n",
    "* red $\\varepsilon^1$: $\\omega_0^2\\left(x_1''+x_1\\right) =\n",
    "  -k_1 x_0'' - x_0^3$.\n",
    "\n",
    "Desno stran razvijemo po $\\cos\\tau$ in $\\cos3\\tau$ (iz $\\cos^3\\tau =\n",
    "\\tfrac34\\cos\\tau+\\tfrac14\\cos3\\tau$); ker bi člen s $\\cos\\tau$ na desni\n",
    "vzbujal ravno lastno nihanje enačbe za $x_1$ (resonanca), bi povzročil\n",
    "neomejeno rast $x_1$ -- zato mora njegov koeficient izginiti. Ta pogoj\n",
    "reši sympy namesto ročnega računa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7a8a08bd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:04.146819Z",
     "iopub.status.busy": "2026-09-25T06:49:04.146695Z",
     "iopub.status.idle": "2026-09-25T06:49:04.406598Z",
     "shell.execute_reply": "2026-09-25T06:49:04.406097Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 A^{2}}{4}$"
      ],
      "text/plain": [
       "3*A**2/4"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "import sympy as sp\n",
    "from sympy.simplify.fu import TR8\n",
    "\n",
    "tau, A, k1 = sp.symbols(\"tau A k1\", positive=True)\n",
    "\n",
    "x0_lp = A * sp.cos(tau)\n",
    "x0_lp_pp = sp.diff(x0_lp, tau, 2)\n",
    "\n",
    "desna_stran = sp.expand(TR8(sp.expand(-k1 * x0_lp_pp - x0_lp**3)))\n",
    "koef_cos1 = desna_stran.coeff(sp.cos(tau))\n",
    "koef_cos3 = desna_stran.coeff(sp.cos(3 * tau))\n",
    "\n",
    "k1_resitev = sp.solve(sp.Eq(koef_cos1, 0), k1)[0]\n",
    "k1_resitev"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b517ce51",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Sympy potrdi znano razmerje $k_1 = \\tfrac34 A^2$, torej\n",
    "\n",
    "$$ \\omega_{\\mathrm{LP}} = \\sqrt{\\omega_0^2 + \\tfrac34\\varepsilon A_0^2}. $$\n",
    "\n",
    "Preostali del desne strani ($-\\tfrac14 A^3\\cos3\\tau$) ni resonanten in da\n",
    "delno rešitev prvega reda $x_1 = \\dfrac{A^3}{32\\,\\omega_0^2}\\cos3\\tau$ --\n",
    "prav ta člen je vir tretjega harmonika, ki smo ga videli v spektru zgoraj."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8490d1d3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:04.407820Z",
     "iopub.status.busy": "2026-09-25T06:49:04.407633Z",
     "iopub.status.idle": "2026-09-25T06:49:04.411926Z",
     "shell.execute_reply": "2026-09-25T06:49:04.411443Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{\\frac{3 A^{2} \\epsilon}{4} + \\omega_{0}^{2}}$"
      ],
      "text/plain": [
       "sqrt(3*A**2*epsilon/4 + omega0**2)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "w_lp_formula = sp.sqrt(sp.symbols(\"omega0\", positive=True) ** 2 + sp.symbols(\"epsilon\") * k1_resitev)\n",
    "w_lp_formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "669b98ff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:04.412955Z",
     "iopub.status.busy": "2026-09-25T06:49:04.412841Z",
     "iopub.status.idle": "2026-09-25T06:49:04.415221Z",
     "shell.execute_reply": "2026-09-25T06:49:04.414772Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lindstedt-Poincaré:  f_LP  = 12.6211214291 Hz\n"
     ]
    }
   ],
   "source": [
    "\n",
    "omega_lp = np.sqrt(w0**2 + eps * (3 / 4) * A0**2)\n",
    "f_lp = omega_lp / (2 * np.pi)\n",
    "print(f\"Lindstedt-Poincaré:  f_LP  = {f_lp:.10f} Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "307eb621",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Primerjava z eksaktno in numerično frekvenco\n",
    "\n",
    "Eksaktno frekvenco proste nihajke z ohranjeno energijo dobimo z istim\n",
    "postopkom kot pri nihalu -- z integralom periode prek potenciala\n",
    "$V(x)=\\tfrac12\\omega_0^2x^2+\\tfrac14\\varepsilon x^4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "25bc40dc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:04.416262Z",
     "iopub.status.busy": "2026-09-25T06:49:04.416146Z",
     "iopub.status.idle": "2026-09-25T06:49:04.570955Z",
     "shell.execute_reply": "2026-09-25T06:49:04.570419Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lindstedt-Poincaré: f_LP        = 12.621121 Hz\n",
      "eksaktna (kvadratura):  f_eks   = 12.584487 Hz\n",
      "numerična (solve_ivp):  f_num   = 12.571429 Hz\n",
      "relativna napaka LP proti eksaktni: 0.29 %\n"
     ]
    }
   ],
   "source": [
    "\n",
    "E0 = 0.5 * w0**2 * A0**2 + 0.25 * eps * A0**4\n",
    "\n",
    "\n",
    "def perioda_duffing_kvad(amplituda):\n",
    "    \"\"\"Eksaktna perioda prostega Duffingovega nihanja z amplitudo `amplituda`.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    amplituda : float\n",
    "        Amplituda nihanja [m] (začetni odmik, hitrost je pri njem nič).\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float\n",
    "        Perioda nihanja [s], izračunana z integracijo energijske relacije.\n",
    "    \"\"\"\n",
    "    energija = 0.5 * w0**2 * amplituda**2 + 0.25 * eps * amplituda**4\n",
    "    integrand = lambda x: 1 / np.sqrt(2 * (energija - 0.5 * w0**2 * x**2 - 0.25 * eps * x**4))\n",
    "    cetrtina, _ = quad(integrand, 0, amplituda, points=[amplituda], limit=200)\n",
    "    return 4 * cetrtina\n",
    "\n",
    "\n",
    "f_eksaktna = 1 / perioda_duffing_kvad(A0)\n",
    "\n",
    "# numerična frekvenca neposredno iz odziva solve_ivp (razmik med vrhovi)\n",
    "from scipy.signal import find_peaks\n",
    "\n",
    "vrhovi, _ = find_peaks(x_niz)\n",
    "f_numericna = 1 / np.mean(np.diff(t_niz[vrhovi]))\n",
    "\n",
    "print(f\"Lindstedt-Poincaré: f_LP        = {f_lp:.6f} Hz\")\n",
    "print(f\"eksaktna (kvadratura):  f_eks   = {f_eksaktna:.6f} Hz\")\n",
    "print(f\"numerična (solve_ivp):  f_num   = {f_numericna:.6f} Hz\")\n",
    "print(f\"relativna napaka LP proti eksaktni: {(f_lp / f_eksaktna - 1) * 100:.2f} %\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c135404d",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Napaka prvega reda Lindstedt-Poincaréja je okrog 0,3 odstotka -- majhna,\n",
    "a ne zanemarljiva. Razlog je v tem, da parameter $\\varepsilon$ tu ni\n",
    "resnično majhen: $\\varepsilon A_0^2/\\omega_0^2 \\approx 0{,}79$, torej je\n",
    "nelinearni prispevek primerljiv z linearnim. Lindstedt-Poincaré je\n",
    "formalno razvoj po majhnem $\\varepsilon$, zato tu deluje le približno --\n",
    "natančnejšo oceno bi dal naslednji red razvoja ($k_2$) ali kar eksaktna\n",
    "kvadratura zgoraj."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca6b8de2",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Duffingov sistem -- vsiljeni sistem s kubično nelinearnostjo\n",
    "\n",
    "Dodamo viskozno dušenje $d$ in harmonsko vzbujanje $F\\cos(\\omega t)$:\n",
    "\n",
    "$$ \\ddot{x} + \\omega_0^2 x + d\\dot{x} + \\varepsilon x^3 = F\\cos(\\omega t). $$\n",
    "\n",
    "Parametri: $F=10000$, $d=20$, $\\omega_0$ in $\\varepsilon$ enaka kot prej."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8bfda1c9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:04.572516Z",
     "iopub.status.busy": "2026-09-25T06:49:04.572390Z",
     "iopub.status.idle": "2026-09-25T06:49:04.727350Z",
     "shell.execute_reply": "2026-09-25T06:49:04.726814Z"
    },
    "lines_to_next_cell": 1
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "d = 20.0\n",
    "F = 10000.0\n",
    "\n",
    "\n",
    "def enacba_vsiljeni_duffing(t, y, w_vzb):\n",
    "    x, v = y\n",
    "    return [v, F * np.cos(w_vzb * t) - w0**2 * x - d * v - eps * x**3]\n",
    "\n",
    "\n",
    "resitev_vsiljena = solve_ivp(\n",
    "    enacba_vsiljeni_duffing, [0, T], [1.0, 0.0], args=(w0,), dense_output=True, rtol=1e-8, atol=1e-10\n",
    ")\n",
    "x_vsiljena = resitev_vsiljena.sol(t_niz)[0]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(t_niz, x_vsiljena, color=\"tab:blue\", linewidth=1.5)\n",
    "ax.set_xlabel(\"t [s]\")\n",
    "ax.set_ylabel(\"x [m]\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f892857",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Frekvenčni odziv s histerezo (skok pri trdi vzmeti)\n",
    "\n",
    "Sledimo izvirnemu postopku: za vsako vzbujalno frekvenco rešimo sistem\n",
    "na intervalu $[0,T]$, amplitudo odčitamo kot maksimum odziva na drugi\n",
    "polovici intervala (približek za ustaljeno stanje), nato pa ta maksimum\n",
    "uporabimo kot začetni odmik za **naslednjo** frekvenco. Ta zvezna\n",
    "nadaljevalna (kontinuacijska) shema pri naraščajočem in padajočem sukanju\n",
    "frekvence sledi drugačni veji odziva -- pojavi se histereza, značilna za\n",
    "trdo (hardening) Duffingovo vzmet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cdef39b3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:49:04.728763Z",
     "iopub.status.busy": "2026-09-25T06:49:04.728636Z",
     "iopub.status.idle": "2026-09-25T06:49:18.640321Z",
     "shell.execute_reply": "2026-09-25T06:49:18.639864Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def dobi_amplitudo(w_vzb, x0_zacetni, T=1.0):\n",
    "    \"\"\"Amplituda ustaljenega odziva vsiljenega Duffingovega sistema.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    w_vzb : float\n",
    "        Krožna frekvenca vzbujanja [rad/s].\n",
    "    x0_zacetni : float\n",
    "        Začetni odmik $x(0)$ -- v kontinuacijski shemi je to amplituda,\n",
    "        dobljena pri prejšnji frekvenci.\n",
    "    T : float, optional\n",
    "        Dolžina simulacije [s].\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float\n",
    "        Maksimalni odmik na drugi polovici intervala $[T/2,T]$.\n",
    "    \"\"\"\n",
    "    sol = solve_ivp(\n",
    "        enacba_vsiljeni_duffing, [0, T], [x0_zacetni, 0.0], args=(w_vzb,),\n",
    "        dense_output=True, rtol=1e-8, atol=1e-10,\n",
    "    )\n",
    "    t_ustaljen = np.linspace(T / 2, T, 501)\n",
    "    return sol.sol(t_ustaljen)[0].max()\n",
    "\n",
    "\n",
    "frekvence_gor = np.arange(1, 61, 1)\n",
    "x0 = 0.01\n",
    "amplitude_gor = []\n",
    "for f in frekvence_gor:\n",
    "    x0 = dobi_amplitudo(f * 2 * np.pi, x0)\n",
    "    amplitude_gor.append(x0)\n",
    "\n",
    "frekvence_dol = np.arange(60, 0, -1)\n",
    "x0 = 0.01\n",
    "amplitude_dol = []\n",
    "for f in frekvence_dol:\n",
    "    x0 = dobi_amplitudo(f * 2 * np.pi, x0)\n",
    "    amplitude_dol.append(x0)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(frekvence_gor, amplitude_gor, color=\"tab:blue\", linewidth=1.5, label=\"naraščajoča frekvenca\")\n",
    "ax.plot(frekvence_dol, amplitude_dol, color=\"tab:red\", linewidth=1.5, label=\"padajoča frekvenca\")\n",
    "ax.set_xlabel(\"f [Hz]\")\n",
    "ax.set_ylabel(\"amplituda x [m]\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  }
 ],
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