20-Lagrange-ProblemasDeFuerzaCentral-GravitacionRelativista.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Problema de Fuerza Centrales: Campo Relativista"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "from matplotlib import pyplot as plt,animation\n",
    "from scipy.integrate import odeint\n",
    "from scipy.optimize import minimize\n",
    "%matplotlib nbagg\n",
    "\n",
    "# Constantes\n",
    "RAD=180/pi\n",
    "DEG=pi/180\n",
    "g=9.8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Potenciales y Fuerzas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def U(r,params):\n",
    "    mu=params[\"mu\"]\n",
    "    h=params[\"h\"]\n",
    "    Rs=params[\"Rs\"]\n",
    "    Upot=-mu/r-Rs*h**2/2*mu/r**3\n",
    "    return Upot\n",
    "\n",
    "def Ueff(r,params):\n",
    "    h=params[\"h\"]\n",
    "    Upot=U(r,params)+h**2/(2*r**2)\n",
    "    return Upot\n",
    "\n",
    "def iUeff(r,params):\n",
    "    if r<0 or r<1 or r>10:\n",
    "        Upot=0\n",
    "    else:\n",
    "        Upot=-Ueff(r,params)\n",
    "    return Upot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gráfica de Potenciales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\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 = $('<div/>');\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",
       "            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",
       "        this.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",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\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 = $('<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 = $('<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 rubberband = $('<canvas/>');\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);\n",
       "        canvas.attr('height', height);\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 = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure()\n",
    "ax=fig.gca()\n",
    "\n",
    "rs=linspace(1e-3,10,1000)\n",
    "\n",
    "params=dict(mu=1,h=10.4,Rs=1.0)\n",
    "ax.plot(rs,U(rs,params),'r--')\n",
    "ax.plot(rs,params[\"h\"]/(2*rs**2),'b--')\n",
    "ax.plot(rs,Ueff(rs,params),'k-')\n",
    "\n",
    "Umax=10\n",
    "ax.set_ylim((-Umax,+Umax))\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Órbitas Circulares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No stable circular orbit\n",
      "Unstable circular orbit at r =  1.52140036447\n"
     ]
    }
   ],
   "source": [
    "solution=minimize(Ueff,[1.0],args=(params,))\n",
    "if solution[\"success\"]:\n",
    "    rcirc=solution[\"x\"][0]\n",
    "    print \"Stable circular orbit at r = \",rcirc\n",
    "else:\n",
    "    print \"No stable circular orbit\"\n",
    "\n",
    "solution=minimize(iUeff,[2.0],args=(params,))\n",
    "if solution[\"success\"]:\n",
    "    rcirc=solution[\"x\"][0]\n",
    "    print \"Unstable circular orbit at r = \",rcirc\n",
    "else:\n",
    "    print \"No unstable circular orbit\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}