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@arsenovic
Created September 30, 2014 17:49
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{
"metadata": {
"name": "",
"signature": "sha256:45fe25fe089abfacf00bae160249c75cf51694d6b04e5ef54f452add67fe55ba"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Orbits"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Demonstration that an ellipse can be constructed from two circular motions of same frequency but oposite rotations."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# JSAnimation import available at https://github.com/jakevdp/JSAnimation\n",
"from JSAnimation import IPython_display\n",
"from matplotlib import animation\n",
"\n",
"# create a simple animation\n",
"fig = plt.figure(figsize = (5,5))\n",
"ax = plt.axes(xlim=(-3, 3), ylim=(-3, 3))\n",
"\n",
"a0 = 1+1j\n",
"b0 = .5+.5j\n",
"\n",
"theta = linspace(0,2*pi,101)\n",
"a = a0*exp(1j*theta)\n",
"b = b0*exp(-1j*theta)\n",
"v = a+b\n",
"i = (a-b)\n",
"\n",
"\n",
"a_line, = ax.plot([], [], 'o-',lw=2, color ='b', label = 'a')\n",
"b_line, = ax.plot([], [], 'o-',lw=2, color='r', label = r'$\\pm$b')\n",
"c_line, = ax.plot([], [], 'o-',lw=2, color='r',label = None)\n",
"v_line, = ax.plot([], [], 'o-',lw=2, color='g', label= 'v')\n",
"i_line, = ax.plot([], [], 'o-',lw=2, color='y', label = 'i')\n",
"primary, = plot(a.real, a.imag)\n",
"secondary, = plot(a0+b.real, a0+b.imag)\n",
"result_v,=plot(v.real, v.imag)\n",
"result_i,=plot(i.real, i.imag)\n",
"\n",
"global lines\n",
"lines = [a_line,b_line,c_line, v_line,i_line]\n",
"\n",
"def init():\n",
" \n",
" global lines\n",
" [k.set_data([], []) for k in lines]\n",
" plot()\n",
" legend()\n",
" \n",
" return lines,\n",
"\n",
"def animate(k):\n",
" global lines\n",
" a_line.set_data([0,a[k].real],[0,a[k].imag])\n",
" b_line.set_data([a[k].real,v[k].real],[a[k].imag,v[k].imag])\n",
" c_line.set_data([a[k].real,i[k].real],[a[k].imag,i[k].imag])\n",
" v_line.set_data([0,v[k].real],[0,v[k].imag])\n",
" i_line.set_data([0,i[k].real],[0,i[k].imag])\n",
" secondary.set_data([a[k].real+b.real,a[k].imag+b.imag])\n",
" g = b[k]/a[k]\n",
" ax,=fig.get_axes()\n",
" ax.set_title(r'$\\Gamma = %.1f +%.1fj$, $\\theta =%.1f \\pi$'%(g.real,g.imag,theta[k]/pi))\n",
" return lines,\n",
"\n",
"animation.FuncAnimation(fig, animate, len(theta), init_func=init,\n",
" interval=40, blit=True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"<script language=\"javascript\">\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" } \n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<div class=\"animation\" align=\"center\">\n",
" <img id=\"_anim_imgKWDYCPQINSMSEWCE\">\n",
" <br>\n",
" <input id=\"_anim_sliderKWDYCPQINSMSEWCE\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animKWDYCPQINSMSEWCE.set_frame(parseInt(this.value));\"></input>\n",
" <br>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.slower()\">&#8211;</button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"rV+/blxKMZUnLgAAAABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"\"></button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"vs7+jud0UcuyL3QAkuEMx4rnIvBYq1JhEwPAUb3fG7x8tVdc292/7Po7f2VqA+Yz7ZwAAAAASUVO\n",
"RK5CYII=\n",
"\"></button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
"j8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkR91DQ2AAAAKtJREFUKM9jYCAN\n",
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"AABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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"Rpcle+Mf8wvgJ16zo/4BtQAAAABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
"j8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkd/uac8wAAAMhJREFUKM9jYBie\n",
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"qNIwUMDAwMDAsADKS2NkGL4AAIARMlfNIfZMAAAAAElFTkSuQmCC\n",
"\"></button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
"j8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAknOOpFQQAAAS9JREFUKM/dkrEv\n",
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"FnSONdiL8Qci0lzwpOM5sQAAAABJRU5ErkJggg==\n",
"\"></button>\n",
" <button onclick=\"animKWDYCPQINSMSEWCE.faster()\">+</button>\n",
" <form action=\"#n\" name=\"_anim_loop_selectKWDYCPQINSMSEWCE\" class=\"anim_control\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
" </form>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imgKWDYCPQINSMSEWCE\";\n",
" var slider_id = \"_anim_sliderKWDYCPQINSMSEWCE\";\n",
" var loop_select_id = \"_anim_loop_selectKWDYCPQINSMSEWCE\";\n",
" var frames = new Array(0);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAYAAAC+ZpjcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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