{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "previous-correlation", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.linalg import expm\n", "from ipywidgets import interactive\n", "from ipywidgets import FloatSlider" ] }, { "cell_type": "markdown", "id": "quality-directory", "metadata": {}, "source": [ "Tento sešit se zabýví řešením soustavy dvou homogenních lineárních diferenciálních rovnic s konstantními koeficienty. Řešíme tedy soustavu\n", "$$\\eqalign{\n", "\\dot x(t)&=ax(t)+by(t)\\cr\n", "\\dot y(t)&=cx(t)+dy(t)\n", "}$$\n", "\n", "Vektorově se tato soustava dá zapsat ve tvaru\n", "$$\\pmatrix{\\dot x(t)\\cr\\dot y(t)}=\\pmatrix{a&b\\cr c&d}\\pmatrix{x(t)\\cr y(t)}$$\n", "nebo kompaktně $\\dot{\\vec x}(t)=A\\vec x(t)$, kde $A=\\pmatrix{a&b\\cr c&d}$.\n", "\n", "K této soustavě doplníme dvojici počátečních podmínek\n", "$$\\eqalign{\n", "x(0)&=x_0\\cr\n", "y(0)&=y_0}$$\n", "\n", "Řešení soustavy se potom dá zapsat ve tvaru $\\vec x(t)=\\exp(At)\\vec x_0$, kde $\\exp$ je tzv. *maticová exponenciála* a $\\vec x_0$ vektor počátečních podmínek." ] }, { "cell_type": "code", "execution_count": 2, "id": "uniform-contest", "metadata": {}, "outputs": [], "source": [ "A=np.array([ #matice soustavy\n", " [ 1, 1],\n", " [-2, 3]\n", "])\n", "\n", "x0=0 #počáteční podmínka\n", "y0=0.01" ] }, { "cell_type": "markdown", "id": "worst-ancient", "metadata": {}, "source": [ "Následující kód vizualizuje řešení zadané soustavy. Dělá dvě věci:\n", "\n", "Za prvé vykresluje vektorové pole dané soustavou. V každém bodě $\\pmatrix{x\\cr y}$ vykreslíme šipku mířící směrem $\\pmatrix{u\\cr v}=A\\pmatrix{x\\cr y}$. Jedná se o malinko něco jiného než jsme dělali pro jednu rovnici na začátku semestru. Tam jsme měli na vodorovné ose „čas“ (nezávisle proměnnou) a na svislé ose neznámou funkci. Teď v tomto případě máme na vodorovné a na svislé ose ony dvě neznámé funkce $x(t)$ a $y(t)$ a čas se v grafu vůbec nevyskytuje. Nevadí to, protože soustava je autonomní, takže vektorové pole vypadá v každém čase stejně (srov. se situací pro jednu rovnici). V případě s jednou rovnicí jsme měli všechny šipky stejně dlouhé a jejich směr nám ukazoval, jak moc řešení roste. Teď když v grafu nemáme čas, tak rychlost růstu (rychlost pohybu) nemůžeme značit vhodným směrem, místo toho máme různě dlouhé šipky. (Čím delší šipka, tím rychleji se bod pohybuje v čase.) Směr šipky pak určuje směr pohybu.\n", "\n", "Za druhé vyřešíme soustavu se zadanou počáteční podmínkou. V grafu je modře zvýrazněn bod o souřadnicích $\\pmatrix{x_0\\cr y_0}$, tj. daný počáteční podmínkou v čase $t=0$. Pohybem slideru pod obrázkem můžete zvětšit čas $t$ a podívat se, kam se bod posouvá. Měl by se vždy posouvat ve směru šipek." ] }, { "cell_type": "code", "execution_count": 3, "id": "compound-toilet", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "872333a9477444ecbe092c0d13c961e4", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.0, description='t', max=3.0, step=0.01), Output()), _dom_classes=('w…" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "x,y = np.meshgrid(np.linspace(-2,2,21),np.linspace(-2,2,21))\n", "u=A[0,0]*x+A[0,1]*y\n", "v=A[1,0]*x+A[1,1]*y\n", "\n", "def ptdo(t):\n", " plt.figure(1)\n", " plt.quiver(x,y,u,v)\n", " [x1,y1]=np.matmul(expm(A*t),[x0,y0])\n", " pt,=plt.plot(x1,y1,marker=\"o\")\n", " plt.xlim(-2,2)\n", " plt.ylim(-2,2)\n", " plt.show()\n", "\n", "\n", "interactive_plot = interactive(ptdo, t=FloatSlider(min=0, max=3, step=0.01, value=0))\n", "interactive_plot" ] }, { "cell_type": "markdown", "id": "iraqi-habitat", "metadata": {}, "source": [ "Tip na hraní: Zadejte jako $A$ nějakou matici s reálnými vlastními čísly. (Třeba první příklad ze cvičení.) Teď když jako počáteční podmínku zadáte vlastní vektor příslušný nějakému vlastnímu číslu $\\lambda$, tak by při časovém vývoji bod měl zůstat v daném vlastním podprostoru; pohybuje se tedy po přímce. Je-li $\\lambda<0$, pak se přibližuje ke středu, naopak pro $\\lambda>0$ diverguje pryč.\n", "\n", "Zkuste jako počáteční podmínku rovněž něco velmi blízkého počátku a ověřte, že funguje kriterium stability stacionárního řešení." ] }, { "cell_type": "code", "execution_count": null, "id": "fallen-better", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }