{ "cells": [ { "cell_type": "markdown", "id": "structural-cooking", "metadata": {}, "source": [ "Non-autonomous systems\n", "======================\n", "\n", "All the ODE systems we have used in the examples thus far belong to the class of autonomous systems.\n", "That is, the time variable $t$ never appears explicitly in the expressions of the right-hand sides of the\n", "ODEs. In this section, we will see how non-autonomous systems can be defined and integrated in heyoka.py.\n", "\n", "The dynamical system we will be focusing on is, again, a pendulum, but this time we will\n", "spice things up a little by introducing a velocity-dependent damping effect and a time-dependent\n", "external forcing. These additional effects create a rich and complex dynamical picture\n", "which is highly sensitive to the initial conditions. See [here](http://pi.math.cornell.edu/~hubbard/pendulum.pdf)\n", "for a detailed analysis of this dynamical system.\n", "\n", "The ODE system of the forced damped pendulum reads:\n", "\n", "$$\n", " \\begin{cases}\n", " x^\\prime = v \\\\\n", " v^\\prime = \\cos t - 0.1v - \\sin(x)\n", " \\end{cases}.\n", "$$\n", "\n", "The $\\cos t$ term represents a periodic time-dependent forcing, while $-0.1v$\n", "is a linear drag representing the effect of air on the pendulum's bob. We take as initial conditions\n", "\n", "$$\n", " \\begin{cases}\n", " x\\left( 0 \\right) = 0 \\\\\n", " v\\left( 0 \\right) = 1.85\n", " \\end{cases}.\n", "$$\n", "\n", "That is, the pendulum is initially in the vertical position with a positive velocity.\n", "\n", "The time variable is represented in heyoka.py's expression system by a special placeholder\n", "called, in a dizzying display of inventiveness, ``time``. Because the name ``time`` is fairly\n", "common, it is generally a good idea\n", "to prepend the module name ``heyoka`` (or its usual abbreviation, ``hy``) when using\n", "the ``time`` expression, in order to avoid ambiguities.\n", "With that in mind, let's look at how the forced damped pendulum is defined in heyoka.py:" ] }, { "cell_type": "code", "execution_count": 1, "id": "legitimate-jumping", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Taylor order: 20\n", "Dimension : 2\n", "Time : 0.0000000000000000\n", "State : [0.0000000000000000, 1.8500000000000001]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import heyoka as hy\n", "\n", "# Create the symbolic variables x and v.\n", "x, v = hy.make_vars(\"x\", \"v\")\n", "\n", "# Create the integrator object.\n", "ta = hy.taylor_adaptive(\n", " # Definition of the ODE system:\n", " # x' = v\n", " # v' = cos(t) - 0.1*v - sin(x)\n", " sys = [(x, v),\n", " (v, hy.cos(hy.time) - .1 * v - hy.sin(x))],\n", " # Initial conditions for x and v.\n", " state = [0., 1.85],\n", " # Explicitly specify the\n", " # initial value for the time\n", " # variable.\n", " time = 0.\n", " )\n", "\n", "ta" ] }, { "cell_type": "markdown", "id": "integrated-logging", "metadata": {}, "source": [ "Note that, for the sake of completeness, we passed an explicit initial value for the time\n", "variable via the keyword argument ``time``. In this specific case, this is superfluous,\n", "as the default initial value for the time variable is already zero.\n", "\n", "We can now integrate the system for a few time units, checking how the value of $x$\n", "varies in time:" ] }, { "cell_type": "code", "execution_count": 2, "id": "swiss-hospital", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib.pylab import plt\n", "plt.rcParams[\"figure.figsize\"] = (12,6)\n", "\n", "# Construct a time grid from t=0 to t=200.\n", "t_grid = np.linspace(0, 200, 1000)\n", "\n", "# Propagate over the time grid.\n", "x_hist = ta.propagate_grid(t_grid)[4][:,0]\n", "\n", "# Display the time evolution for the x variable.\n", "plt.plot(t_grid, x_hist)\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"x\");" ] }, { "cell_type": "markdown", "id": "magnetic-savings", "metadata": {}, "source": [ "After an initial excursion to higher values for $x$, the system seems to settle into a stable motion. Note that, because this system can exhibit chaotic behaviour, changing\n", "the initial conditions by a small amount might lead to a qualitatively-different long-term behaviour." ] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }