{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "This code was authored by Alex Shvonski, Copyright 2020 MIT All Rights Reserved.\n", "
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Initializing the program

\n", "\n", "To initialize the visualization, you may need to click \"Run all initialization cells\" above (see button location in figure).\n", "\n", "\"Drawing\"\n", "\n", "
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\n", "You should see the visualization directly below this line, before the next section.\n", "\n", "
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" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "init_cell": true }, "outputs": [], "source": [ "#This code was authored by Alex Shvonski, Copyright 2020 MIT All Rights Reserved.\n", "\n", "%matplotlib notebook\n", "import ipywidgets as widgets\n", "from IPython.display import display, clear_output\n", "from ipywidgets import interact, interactive, interactive_output, fixed, IntSlider, HBox, Layout, Output, VBox\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.animation import FuncAnimation\n", "import matplotlib.animation as animation\n", "from math import pi\n", "\n", "pause = True" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "init_cell": true }, "outputs": [], "source": [ "#Define functions\n", "###############################################\n", "###############################################\n", "def omega_1(g,l,k,m):\n", " return np.sqrt(g/l)\n", "\n", "def omega_2(g,l,k,m):\n", " return np.sqrt((g/l) + (2*k/m))\n", "\n", "def alpha_f(x1_0, x2_0, v1_0, v2_0):\n", " om1 = omega_1(g,l,k,m)\n", " result = 0.5*np.sqrt((x1_0 + x2_0)**2. + ((v1_0 + v2_0)/om1)**2.)\n", " return result\n", "\n", "def beta_f(x1_0, x2_0, v1_0, v2_0):\n", " om2 = omega_2(g,l,k,m)\n", " result = 0.5*np.sqrt((x1_0 - x2_0)**2. + ((v1_0 - v2_0)/om2)**2.)\n", " return result\n", "\n", "def phi1_f(x1_0, x2_0, v1_0, v2_0):\n", " om1 = omega_1(g,l,k,m)\n", " #result = arctan((-1/om)*(v1+v2)/(x1+x2))\n", " result = np.arctan2(-(v1_0+v2_0),om1*(x1_0+x2_0))\n", " return result\n", "\n", "def phi2_f(x1_0, x2_0, v1_0, v2_0):\n", " om2 = omega_2(g,l,k,m)\n", " #result = arctan((-1/om)*(v1+v2)/(x1+x2))\n", " result = np.arctan2(-(v1_0-v2_0),om2*(x1_0-x2_0))\n", " return result\n", "\n", "def B1_f(wd,g,l,k,m):\n", " om1 = omega_1(g,l,k,m)\n", " om2 = omega_2(g,l,k,m)\n", " result = (F0/m)*((k/m) + (g/l) - wd**2.)/((wd**2. - om1**2.)*(wd**2. - om2**2.))\n", " return result\n", "\n", "def B2_f(wd,g,l,k,m):\n", " om1 = omega_1(g,l,k,m)\n", " om2 = omega_2(g,l,k,m)\n", " result = (F0/m)*(k/m)/((wd**2. - om1**2.)*(wd**2. - om2**2.))\n", " return result\n", "\n", "def general_sol(t,g,l,k,m,x1_0,x2_0,v1_0,v2_0,wd):\n", " om1 = omega_1(g,l,k,m)\n", " om2 = omega_2(g,l,k,m)\n", " phi1 = phi1_f(x1_0, x2_0, v1_0, v2_0)\n", " phi2 = phi2_f(x1_0, x2_0, v1_0, v2_0)\n", " alpha = alpha_f(x1_0, x2_0, v1_0, v2_0)\n", " beta = beta_f(x1_0, x2_0, v1_0, v2_0)\n", " B1 = B1_f(wd,g,l,k,m)\n", " B2 = B2_f(wd,g,l,k,m)\n", " x1 = alpha*np.cos(om1*t + phi1) + beta*np.cos(om2*t + phi2) + B1*np.cos(wd*t)\n", " x2 = alpha*np.cos(om1*t + phi1) - beta*np.cos(om2*t + phi2) + B2*np.cos(wd*t)\n", " return x1, x2\n", "\n", "def F_drive(t,wd):\n", " return F0*np.cos(wd*t)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "init_cell": true }, "outputs": [], "source": [ "def simData():\n", " global t0#, x1_nm1, x2_nm1, x1_nm2, x2_nm2, x1_gen, x2_gen\n", "\n", " t = np.linspace(0., 15., 1000)\n", " t_max = max(t)\n", " dt = t[1]-t[0]\n", " #t_max = 15.\n", " #dt = 0.01\n", " t0 = 0\n", " \n", " while t0 < t_max:\n", " if not pause:\n", " t0 = t0 + dt\n", " yield t0\n", " \n", "def simPoints(simData):\n", " #t0, x1_nm1, x2_nm1, x1_nm2, x2_nm2, x1_gen, x2_gen = simData\n", " t0 = simData\n", " \n", " #plot1\n", " ############################# \n", " line_1.set_data(t,general_sol(t,g,l,k,m,x1_0,x2_0,v1_0,v2_0,wd)[0])\n", " line_2.set_data(t,general_sol(t,g,l,k,m,x1_0,x2_0,v1_0,v2_0,wd)[1])\n", " vert_line_1.set_data([t0,t0],[-y_max_3,y_max_3])\n", "\n", " #plot2\n", " ############################# \n", " line_3.set_data(t,F_drive(t,wd))\n", " vert_line_2.set_data([t0,t0],[-y_max_3,y_max_3])\n", " \n", " #plot3\n", " ############################# \n", " line_4.set_data(general_sol(t0,g,l,k,m,x1_0,x2_0,v1_0,v2_0,wd)[0] - 1.25, 0.)\n", " line_5.set_data(general_sol(t0,g,l,k,m,x1_0,x2_0,v1_0,v2_0,wd)[1] + 1.25, 0.)\n", " \n", " #plot4\n", " ############################# \n", " #line_6.set_data(F_drive(t0,wd) - 1.25, 0.)\n", " line_6.set_data([-1.25, -1.25 + F_drive(t0,wd)], [0., 0.])\n", " \n", " #plot5\n", " ############################# \n", " line_7.set_data(wd_range,B1_f(wd_range,g,l,k,m))\n", " line_8.set_data(wd_range,B2_f(wd_range,g,l,k,m))\n", " vert_line_3.set_data([wd,wd],[-y_max_3,y_max_3])\n", " \n", " \n", " return line_1, line_2, vert_line_1, line_3, vert_line_2, line_4, line_5, line_6, line_7, line_8, vert_line_3" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "init_cell": true }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " if (mpl.ratio != 1) {\n", " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", " }\n", " fig.send_message(\"refresh\", {});\n", " }\n", "\n", " this.imageObj.onload = function() {\n", " if (fig.image_mode == 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function() {\n", " fig.ws.close();\n", " }\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "}\n", "\n", "mpl.figure.prototype._init_header = function() {\n", " var titlebar = $(\n", " '
');\n", " var titletext = $(\n", " '
');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('
');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var backingStore = this.context.backingStorePixelRatio ||\n", "\tthis.context.webkitBackingStorePixelRatio ||\n", "\tthis.context.mozBackingStorePixelRatio ||\n", "\tthis.context.msBackingStorePixelRatio ||\n", "\tthis.context.oBackingStorePixelRatio ||\n", "\tthis.context.backingStorePixelRatio || 1;\n", "\n", " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width * mpl.ratio);\n", " canvas.attr('height', height * mpl.ratio);\n", " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
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