{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d3a009e5",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# Višja dinamika -- Zvezni sistemi\n",
    "\n",
    "Dr. Janko Slavič, april 2013 (prevod izvirnega Mathematica zvezka v\n",
    "Python)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fa50c41",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## 1. naloga -- Nihanje gredi z dodanim vztrajnikom\n",
    "\n",
    "### Reševanje transcendentne enačbe\n",
    "\n",
    "Gred je na enem koncu vpeta, na prostem koncu pa nosi vztrajnik z masnim\n",
    "vztrajnostnim momentom $J\\s{v}$. Robni pogoj na prostem koncu izenači\n",
    "moment gredi zaradi zasuka z vztrajnostnim momentom vztrajnika, kar vodi\n",
    "do transcendentne frekvenčne enačbe\n",
    "\n",
    "$$ \\tan\\alpha = \\frac{\\beta}{\\alpha}, $$\n",
    "\n",
    "kjer je $\\alpha = \\omega l / c$ brezrazsežni frekvenčni parameter\n",
    "($c$ je hitrost torzijskega vala po gredi) in $\\beta = J\\s{gred}/J\\s{v}$\n",
    "razmerje med lastnim masnim vztrajnostnim momentom gredi in\n",
    "vztrajnostnim momentom dodanega vztrajnika."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "24cee1e6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:33.553630Z",
     "iopub.status.busy": "2026-09-25T06:45:33.553523Z",
     "iopub.status.idle": "2026-09-25T06:45:33.735924Z",
     "shell.execute_reply": "2026-09-25T06:45:33.734972Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\tan{\\left(\\alpha \\right)} = \\frac{\\beta}{\\alpha}$"
      ],
      "text/plain": [
       "Eq(tan(alpha), beta/alpha)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "import sympy as sp\n",
    "\n",
    "alpha, beta = sp.symbols(\"alpha beta\", positive=True)\n",
    "enacba = sp.Eq(sp.tan(alpha), beta / alpha)\n",
    "enacba"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eda0c2c",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Ničle enačbe so presečišča grafov $\\tan\\alpha$ in $\\beta/\\alpha$; za\n",
    "nazoren prikaz vzemimo $\\beta = 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2cc03b70",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:33.738155Z",
     "iopub.status.busy": "2026-09-25T06:45:33.737974Z",
     "iopub.status.idle": "2026-09-25T06:45:34.252533Z",
     "shell.execute_reply": "2026-09-25T06:45:34.251885Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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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",
    "alfa_zvezni = np.linspace(1e-3, 6, 4000)\n",
    "# tan ima pole pri (2k-1) pi/2 -- tam vrednosti odrežemo, da graf ne\n",
    "# povezuje vej čez neskončnost\n",
    "tan_vrednosti = np.tan(alfa_zvezni)\n",
    "tan_vrednosti[np.abs(np.cos(alfa_zvezni)) < 1e-2] = np.nan\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(alfa_zvezni, tan_vrednosti, color=\"tab:blue\", linewidth=1.5, label=r\"$\\tan\\alpha$\")\n",
    "ax.plot(alfa_zvezni, 1 / alfa_zvezni, color=\"tab:red\", linewidth=1.5, label=r\"$1/\\alpha$\")\n",
    "ax.set_xlim(0, 6)\n",
    "ax.set_ylim(-2, 2)\n",
    "ax.set_xlabel(r\"$\\alpha$\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "377f503d",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Numerično iskanje ničel\n",
    "\n",
    "Ker ima $\\tan\\alpha$ pole pri $\\alpha = (2k-1)\\pi/2$, iskanje ničel\n",
    "razdelimo na intervale med zaporednimi poli, znotraj vsakega pa na\n",
    "gosti mreži poiščemo spremembo predznaka in jo natančno določimo z\n",
    "`brentq`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2662d0d6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:34.253848Z",
     "iopub.status.busy": "2026-09-25T06:45:34.253694Z",
     "iopub.status.idle": "2026-09-25T06:45:34.441045Z",
     "shell.execute_reply": "2026-09-25T06:45:34.440675Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.8603335890193793, 3.4256184594817283]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from scipy.optimize import brentq\n",
    "\n",
    "\n",
    "def enacba_gredi(alfa_, beta_):\n",
    "    \"\"\"Leva stran frekvenčne enačbe tan(alfa) - beta/alfa = 0.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    alfa_ : float\n",
    "        Brezrazsežni frekvenčni parameter.\n",
    "    beta_ : float\n",
    "        Razmerje vztrajnostnih momentov gredi in vztrajnika.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float\n",
    "        Vrednost leve strani frekvenčne enačbe.\n",
    "    \"\"\"\n",
    "    return np.tan(alfa_) - beta_ / alfa_\n",
    "\n",
    "\n",
    "def poisci_nicle(funkcija, beta_, alfa_max, n_tock=4000):\n",
    "    \"\"\"Poišče ničle transcendentne enačbe tipa tan(alfa) = beta/alfa.\n",
    "\n",
    "    Interval (0, alfa_max) razdeli na podintervale med poli tangensa,\n",
    "    znotraj vsakega podintervala pa z gosto mrežo poišče spremembo\n",
    "    predznaka in jo natančno določi z metodo brentq.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    funkcija : callable\n",
    "        Funkcija oblike funkcija(alfa, beta).\n",
    "    beta_ : float\n",
    "        Parameter beta v frekvenčni enačbi.\n",
    "    alfa_max : float\n",
    "        Zgornja meja iskanja.\n",
    "    n_tock : int\n",
    "        Število točk mreže na posamezen podinterval.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    list of float\n",
    "        Najdene ničle, urejene naraščajoče.\n",
    "    \"\"\"\n",
    "    poli = [(2 * k - 1) * np.pi / 2 for k in range(1, 20) if (2 * k - 1) * np.pi / 2 < alfa_max]\n",
    "    meje = [0.0] + poli + [alfa_max]\n",
    "    rob = 1e-6\n",
    "    nicle = []\n",
    "    for spodnja, zgornja in zip(meje[:-1], meje[1:]):\n",
    "        alfa_mreza = np.linspace(spodnja + rob, zgornja - rob, n_tock)\n",
    "        vrednosti = funkcija(alfa_mreza, beta_)\n",
    "        predznaki = np.sign(vrednosti)\n",
    "        for i in range(len(alfa_mreza) - 1):\n",
    "            if predznaki[i] != predznaki[i + 1] and np.isfinite(vrednosti[i]) and np.isfinite(vrednosti[i + 1]):\n",
    "                nicle.append(brentq(funkcija, alfa_mreza[i], alfa_mreza[i + 1], args=(beta_,)))\n",
    "    return nicle\n",
    "\n",
    "\n",
    "nicle_beta1 = poisci_nicle(enacba_gredi, beta_=1.0, alfa_max=6.0)\n",
    "nicle_beta1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "673177e7",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Prva dva korena za $\\beta = 1$ ($\\alpha_1 \\approx 0{,}860$,\n",
    "$\\alpha_2 \\approx 3{,}426$) ustrezata presečiščema na zgornjem grafu.\n",
    "Isti postopek deluje za poljuben $\\beta$, torej za poljubno razmerje\n",
    "vztrajnostnih momentov gredi in vztrajnika."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8730cf3e",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Struna\n",
    "\n",
    "### Analitična rešitev\n",
    "\n",
    "Za vpeto struno dolžine $l$, napete s silo $P$ in mase na dolžino\n",
    "$m/l$, so lastne frekvence\n",
    "\n",
    "$$ \\omega_k = k \\pi \\frac{c}{l}, \\qquad c = \\sqrt{\\frac{P}{m/l}}. $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7aa4376d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:34.442153Z",
     "iopub.status.busy": "2026-09-25T06:45:34.441993Z",
     "iopub.status.idle": "2026-09-25T06:45:34.444888Z",
     "shell.execute_reply": "2026-09-25T06:45:34.444567Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.22144147,  4.44288294,  6.66432441,  8.88576588, 11.10720735])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "P = 100000.0\n",
    "l = 200.0\n",
    "m = 1000.0\n",
    "\n",
    "c = np.sqrt(P / (m / l))\n",
    "\n",
    "\n",
    "def lastna_frekvenca(k):\n",
    "    \"\"\"Analitična lastna frekvenca vpete strune.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    k : int ali array_like\n",
    "        Zaporedna številka nihajne oblike (k = 1, 2, ...).\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float ali ndarray\n",
    "        Lastna (krožna) frekvenca k-te oblike.\n",
    "    \"\"\"\n",
    "    return k * np.pi * c / l\n",
    "\n",
    "\n",
    "lastne_frekvence_analiticno = lastna_frekvenca(np.arange(1, 6))\n",
    "lastne_frekvence_analiticno"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b354c516",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Vpliv robnega pogoja z vzmetjo\n",
    "\n",
    "Če je struna na prostem koncu podprta z vzmetjo togosti $k$, robni\n",
    "pogoj vodi do frekvenčne enačbe\n",
    "\n",
    "$$ \\frac{P\\omega}{kc} + \\tan\\left(\\frac{\\omega}{c} l\\right) = 0. $$\n",
    "\n",
    "Pri zelo veliki togosti $k$ se rešitev približa rešitvi za vpeto\n",
    "struno -- prikažimo graf leve strani enačbe za $k = 10^{10}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2cb4c0d7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:34.445905Z",
     "iopub.status.busy": "2026-09-25T06:45:34.445807Z",
     "iopub.status.idle": "2026-09-25T06:45:34.509473Z",
     "shell.execute_reply": "2026-09-25T06:45:34.508948Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "k_vzmeti = 1e10\n",
    "\n",
    "omega_zvezno = np.linspace(1e-3, 10, 6000)\n",
    "leva_stran = P * omega_zvezno / (k_vzmeti * c) + np.tan(omega_zvezno / c * l)\n",
    "leva_stran[np.abs(np.cos(omega_zvezno / c * l)) < 1e-2] = np.nan\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(omega_zvezno, leva_stran, color=\"tab:blue\", linewidth=1.5)\n",
    "ax.set_xlabel(r\"$\\omega$\")\n",
    "ax.set_ylabel(r\"$P\\omega/(kc) + \\tan(\\omega l/c)$\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd74efd6",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Ničle so pri $\\omega \\approx k\\pi c/l$, torej pri skoraj enakih\n",
    "vrednostih kot pri vpeti struni -- toga vzmet je dobra približna\n",
    "nadomestitev za togo vpetje."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a36ae15e",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Diskretizacija\n",
    "\n",
    "Struno nadomestimo z $n$ točkastimi masami, povezanimi v verigo med\n",
    "dvema vpetima krajiščema. Masna matrika je diagonalna, togostna\n",
    "matrika pa ima standardno tridiagonalno obliko [2, -1] (vsaka masa je\n",
    "povezana s sosednjima, krajni masi pa še z vpetjema)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "abdbb739",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:34.511501Z",
     "iopub.status.busy": "2026-09-25T06:45:34.511255Z",
     "iopub.status.idle": "2026-09-25T06:45:34.518691Z",
     "shell.execute_reply": "2026-09-25T06:45:34.517951Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.06016651,  4.10881173,  6.1344788 ,  8.12583939, 10.07175698,\n",
       "       11.96134923, 13.78404875, 15.52966229, 17.18842765, 18.75106835,\n",
       "       20.20884548, 21.55360654, 22.77783109, 23.87467277, 24.8379976 ,\n",
       "       25.66241827, 26.34332428, 26.87690774, 27.26018463, 27.49101151])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from scipy.linalg import eigh\n",
    "\n",
    "n = 20\n",
    "J = m * l / (n * (n - 1) * P)\n",
    "\n",
    "M = J * np.eye(n)\n",
    "\n",
    "K = np.zeros((n, n))\n",
    "for i in range(n):\n",
    "    for j in range(n):\n",
    "        if i == j:\n",
    "            K[i, j] = 2.0\n",
    "        elif abs(i - j) == 1:\n",
    "            K[i, j] = -1.0\n",
    "\n",
    "lastne_vrednosti, oblike_nihanja = eigh(K, M)\n",
    "lastne_frekvence_diskretno = np.sqrt(lastne_vrednosti)\n",
    "lastne_frekvence_diskretno"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f851991",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Primerjava z analitično rešitvijo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6f4ffb6d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:34.520029Z",
     "iopub.status.busy": "2026-09-25T06:45:34.519887Z",
     "iopub.status.idle": "2026-09-25T06:45:34.522708Z",
     "shell.execute_reply": "2026-09-25T06:45:34.522190Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k=1:  analiticno =   2.2214   diskretno (n=20) =   2.0602   razlika =  -7.26 %\n",
      "k=2:  analiticno =   4.4429   diskretno (n=20) =   4.1088   razlika =  -7.52 %\n",
      "k=3:  analiticno =   6.6643   diskretno (n=20) =   6.1345   razlika =  -7.95 %\n",
      "k=4:  analiticno =   8.8858   diskretno (n=20) =   8.1258   razlika =  -8.55 %\n",
      "k=5:  analiticno =  11.1072   diskretno (n=20) =  10.0718   razlika =  -9.32 %\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for k in range(1, 6):\n",
    "    analiticno = lastna_frekvenca(k)\n",
    "    diskretno = lastne_frekvence_diskretno[k - 1]\n",
    "    print(\n",
    "        f\"k={k}:  analiticno = {analiticno:8.4f}   \"\n",
    "        f\"diskretno (n={n}) = {diskretno:8.4f}   \"\n",
    "        f\"razlika = {100 * (diskretno - analiticno) / analiticno:6.2f} %\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d022b17d",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Diskretni model sistematično podceni lastne frekvence (klasična\n",
    "napaka končnih diferenc pri grobi mreži), z večanjem $n$ pa razlika\n",
    "pada proti nič."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b06f402e",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Nihajne oblike\n",
    "\n",
    "Prikažimo prve tri (najnižje) nihajne oblike diskretnega modela."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3b2aadeb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-25T06:45:34.523727Z",
     "iopub.status.busy": "2026-09-25T06:45:34.523618Z",
     "iopub.status.idle": "2026-09-25T06:45:34.588185Z",
     "shell.execute_reply": "2026-09-25T06:45:34.587699Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "for i in range(3):\n",
    "    ax.plot(\n",
    "        np.arange(1, n + 1),\n",
    "        oblike_nihanja[:, i],\n",
    "        linewidth=1.5,\n",
    "        label=f\"oblika {i + 1}\",\n",
    "    )\n",
    "ax.set_xlabel(\"zaporedna številka mase\")\n",
    "ax.set_ylabel(\"amplituda\")\n",
    "ax.grid(True, alpha=0.3)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "formats": "ipynb,py:percent"
  },
  "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": "3.13.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
