{ "cells": [ { "cell_type": "markdown", "id": "analyzed-founder", "metadata": {}, "source": [ "This tutorial presents another example of solving ordinary differential equations using *odeint()*." ] }, { "cell_type": "code", "execution_count": 1, "id": "unusual-income", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint" ] }, { "cell_type": "markdown", "id": "handmade-corporation", "metadata": {}, "source": [ "The differential equation that we will attempt to solve is:\n", "\n", "$\\ddot{z}=-\\dfrac{1}{z}\\left(\\dot{z}^2+b\\dot{z}+gz-gh\\right)$.\n", "\n", "In this expression, $z$ the height of water inside a straw with one end partially submerged in a cup of water. Oscillations of the water level are induced by an initial pressure difference between the inside of the straw and the surface of the water in the cup (at one atmosphere). For more details, see R. P. Smith and E. H. Matlis, *American Journal of Physics* **87**, 433 (2019).\n", "\n", "> $g = 9.81~\\mathrm{m}/\\mathrm{s}^2$
\n", " $h$ is the depth that the straw is submerged in the water
\n", " $b$ is a drag coefficient" ] }, { "cell_type": "code", "execution_count": 2, "id": "frank-investor", "metadata": {}, "outputs": [], "source": [ "g = 9.81 # m/s^2\n", "h = 0.10 # m\n", "b = 0.25 # m/s" ] }, { "cell_type": "markdown", "id": "documented-latvia", "metadata": {}, "source": [ "The strategy to solve a second-order differential equation using *odeint()* is to write the equation as a system of two first-order equations. This is achieved by first writing $x[1] = \\dot{z}$ and $x[0] = z$. In that case, or original second-order equation can be expressed as:\n", "\n", "$\\ddot{z}=\\dot{x}[1]=-\\dfrac{1}{x[0]}\\left(x[1]^2+bx[1]+gx[0]-gh\\right)$.\n", "\n", "One of our first-order equations is the expression above and the other is simply $\\dot{z}=x[1]$. \n", "\n", "- Now, we define a function that returns $\\dot{z}$ and $\\ddot{z}$ (in that order)." ] }, { "cell_type": "code", "execution_count": 3, "id": "modular-payroll", "metadata": {}, "outputs": [], "source": [ "def z_derivatives(x, t):\n", " return [x[1], -(1/x[0])*(x[1]**2 + b*x[1] + g*x[0] - g*h)]" ] }, { "cell_type": "markdown", "id": "patent-costs", "metadata": {}, "source": [ "- Next, we create an array of the desired times for the solution." ] }, { "cell_type": "code", "execution_count": 4, "id": "ancient-edinburgh", "metadata": {}, "outputs": [], "source": [ "time = np.arange(0, 3, 1e-3)" ] }, { "cell_type": "markdown", "id": "tough-landing", "metadata": {}, "source": [ "- Here is the call to *odeint()*. This time we need to pass an array of initial conditions, the first is for $z(0)$ and the second is for $\\dot{z}(0)$. The .T is necessary so that we can separately unpack the solutions as $z(t)$ and $\\dot{z}(t)$ (not intuitive, in my opinion)." ] }, { "cell_type": "code", "execution_count": 5, "id": "cardiac-baseline", "metadata": {}, "outputs": [], "source": [ "position, velocity = odeint(z_derivatives, [2e-3, 0], time).T " ] }, { "cell_type": "markdown", "id": "intellectual-approach", "metadata": {}, "source": [ "- A plot of the fluid height (position) inside the straw as a function of time." ] }, { "cell_type": "code", "execution_count": 6, "id": "junior-driving", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(time, position*100, 'orange', linewidth = 2)\n", "plt.xlabel('time (s)')\n", "plt.ylabel('position (cm)')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "id": "unavailable-browse", "metadata": {}, "source": [ "- A plot of the fluid velcoity as a function of time." ] }, { "cell_type": "code", "execution_count": 7, "id": "intellectual-employer", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(time, velocity*100, 'blue', linewidth = 2)\n", "plt.xlabel('time (s)')\n", "plt.ylabel('velocity (cm/s)')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.grid(True)\n", "plt.axis((0, 3, -30, 80));" ] }, { "cell_type": "markdown", "id": "durable-librarian", "metadata": {}, "source": [ "- We can call our function to access $\\ddot{z}$ (the acceleration). The _, is just a place holder for a variable that we're not going to use. That part of the model returns $\\dot{z}$, but we already have that solution from 'odeint'." ] }, { "cell_type": "code", "execution_count": 8, "id": "false-judge", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_, a = z_derivatives([position, velocity], time)\n", "plt.plot(time, a, 'cyan', linewidth = 2)\n", "plt.xlabel('time (s)')\n", "plt.ylabel('acceleration (m/s^2)')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.grid(True)\n", "plt.axis((0, 3, -3, 4));" ] } ], "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": "3.9.15" } }, "nbformat": 4, "nbformat_minor": 5 }