{ "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": [ "C++ datatype : double\n", "Tolerance : 2.220446049250313e-16\n", "High accuracy : false\n", "Compact mode : false\n", "Taylor order : 20\n", "Dimension : 2\n", "Time : 0\n", "State : [0, 1.85]" ] }, "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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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib.pylab import plt\n", "\n", "fig = plt.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)[5][:,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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 5 }