.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_gallery_animation_double_pendulum.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_gallery_animation_double_pendulum.py:


===========================
The double pendulum problem
===========================

This animation illustrates the double pendulum problem.

Double pendulum formula translated from the C code at
http://www.physics.usyd.edu.au/~wheat/dpend_html/solve_dpend.c



.. only:: builder_html

    .. container:: sphx-glr-animation

        .. raw:: html

            
         <link rel="stylesheet"
         href="https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css">
         <script language="javascript">
           function isInternetExplorer() {
             ua = navigator.userAgent;
             /* MSIE used to detect old browsers and Trident used to newer ones*/
             return ua.indexOf("MSIE ") > -1 || ua.indexOf("Trident/") > -1;
           }

           /* Define the Animation class */
           function Animation(frames, img_id, slider_id, interval, loop_select_id){
             this.img_id = img_id;
             this.slider_id = slider_id;
             this.loop_select_id = loop_select_id;
             this.interval = interval;
             this.current_frame = 0;
             this.direction = 0;
             this.timer = null;
             this.frames = new Array(frames.length);

             for (var i=0; i<frames.length; i++)
             {
              this.frames[i] = new Image();
              this.frames[i].src = frames[i];
             }
             var slider = document.getElementById(this.slider_id);
             slider.max = this.frames.length - 1;
             if (isInternetExplorer()) {
                 // switch from oninput to onchange because IE <= 11 does not conform
                 // with W3C specification. It ignores oninput and onchange behaves
                 // like oninput. In contrast, Microsoft Edge behaves correctly.
                 slider.setAttribute('onchange', slider.getAttribute('oninput'));
                 slider.setAttribute('oninput', null);
             }
             this.set_frame(this.current_frame);
           }

           Animation.prototype.get_loop_state = function(){
             var button_group = document[this.loop_select_id].state;
             for (var i = 0; i < button_group.length; i++) {
                 var button = button_group[i];
                 if (button.checked) {
                     return button.value;
                 }
             }
             return undefined;
           }

           Animation.prototype.set_frame = function(frame){
             this.current_frame = frame;
             document.getElementById(this.img_id).src =
                     this.frames[this.current_frame].src;
             document.getElementById(this.slider_id).value = this.current_frame;
           }

           Animation.prototype.next_frame = function()
           {
             this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));
           }

           Animation.prototype.previous_frame = function()
           {
             this.set_frame(Math.max(0, this.current_frame - 1));
           }

           Animation.prototype.first_frame = function()
           {
             this.set_frame(0);
           }

           Animation.prototype.last_frame = function()
           {
             this.set_frame(this.frames.length - 1);
           }

           Animation.prototype.slower = function()
           {
             this.interval /= 0.7;
             if(this.direction > 0){this.play_animation();}
             else if(this.direction < 0){this.reverse_animation();}
           }

           Animation.prototype.faster = function()
           {
             this.interval *= 0.7;
             if(this.direction > 0){this.play_animation();}
             else if(this.direction < 0){this.reverse_animation();}
           }

           Animation.prototype.anim_step_forward = function()
           {
             this.current_frame += 1;
             if(this.current_frame < this.frames.length){
               this.set_frame(this.current_frame);
             }else{
               var loop_state = this.get_loop_state();
               if(loop_state == "loop"){
                 this.first_frame();
               }else if(loop_state == "reflect"){
                 this.last_frame();
                 this.reverse_animation();
               }else{
                 this.pause_animation();
                 this.last_frame();
               }
             }
           }

           Animation.prototype.anim_step_reverse = function()
           {
             this.current_frame -= 1;
             if(this.current_frame >= 0){
               this.set_frame(this.current_frame);
             }else{
               var loop_state = this.get_loop_state();
               if(loop_state == "loop"){
                 this.last_frame();
               }else if(loop_state == "reflect"){
                 this.first_frame();
                 this.play_animation();
               }else{
                 this.pause_animation();
                 this.first_frame();
               }
             }
           }

           Animation.prototype.pause_animation = function()
           {
             this.direction = 0;
             if (this.timer){
               clearInterval(this.timer);
               this.timer = null;
             }
           }

           Animation.prototype.play_animation = function()
           {
             this.pause_animation();
             this.direction = 1;
             var t = this;
             if (!this.timer) this.timer = setInterval(function() {
                 t.anim_step_forward();
             }, this.interval);
           }

           Animation.prototype.reverse_animation = function()
           {
             this.pause_animation();
             this.direction = -1;
             var t = this;
             if (!this.timer) this.timer = setInterval(function() {
                 t.anim_step_reverse();
             }, this.interval);
           }
         </script>

         <style>
         .animation {
             display: inline-block;
             text-align: center;
         }
         input[type=range].anim-slider {
             width: 374px;
             margin-left: auto;
             margin-right: auto;
         }
         .anim-buttons {
             margin: 8px 0px;
         }
         .anim-buttons button {
             padding: 0;
             width: 36px;
         }
         .anim-state label {
             margin-right: 8px;
         }
         .anim-state input {
             margin: 0;
             vertical-align: middle;
         }
         </style>

         <div class="animation">
           <img id="_anim_img2bee0e98b0754400bc53cc76e7a81e2a">
           <div class="anim-controls">
             <input id="_anim_slider2bee0e98b0754400bc53cc76e7a81e2a" type="range" class="anim-slider"
                    name="points" min="0" max="1" step="1" value="0"
                    oninput="anim2bee0e98b0754400bc53cc76e7a81e2a.set_frame(parseInt(this.value));"></input>
             <div class="anim-buttons">
               <button title="Decrease speed" aria-label="Decrease speed" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.slower()">
                   <i class="fa fa-minus"></i></button>
               <button title="First frame" aria-label="First frame" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.first_frame()">
                 <i class="fa fa-fast-backward"></i></button>
               <button title="Previous frame" aria-label="Previous frame" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.previous_frame()">
                   <i class="fa fa-step-backward"></i></button>
               <button title="Play backwards" aria-label="Play backwards" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.reverse_animation()">
                   <i class="fa fa-play fa-flip-horizontal"></i></button>
               <button title="Pause" aria-label="Pause" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.pause_animation()">
                   <i class="fa fa-pause"></i></button>
               <button title="Play" aria-label="Play" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.play_animation()">
                   <i class="fa fa-play"></i></button>
               <button title="Next frame" aria-label="Next frame" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.next_frame()">
                   <i class="fa fa-step-forward"></i></button>
               <button title="Last frame" aria-label="Last frame" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.last_frame()">
                   <i class="fa fa-fast-forward"></i></button>
               <button title="Increase speed" aria-label="Increase speed" onclick="anim2bee0e98b0754400bc53cc76e7a81e2a.faster()">
                   <i class="fa fa-plus"></i></button>
             </div>
             <form title="Repetition mode" aria-label="Repetition mode" action="#n" name="_anim_loop_select2bee0e98b0754400bc53cc76e7a81e2a"
                   class="anim-state">
               <input type="radio" name="state" value="once" id="_anim_radio1_2bee0e98b0754400bc53cc76e7a81e2a"
                      >
               <label for="_anim_radio1_2bee0e98b0754400bc53cc76e7a81e2a">Once</label>
               <input type="radio" name="state" value="loop" id="_anim_radio2_2bee0e98b0754400bc53cc76e7a81e2a"
                      checked>
               <label for="_anim_radio2_2bee0e98b0754400bc53cc76e7a81e2a">Loop</label>
               <input type="radio" name="state" value="reflect" id="_anim_radio3_2bee0e98b0754400bc53cc76e7a81e2a"
                      >
               <label for="_anim_radio3_2bee0e98b0754400bc53cc76e7a81e2a">Reflect</label>
             </form>
           </div>
         </div>


         <script language="javascript">
           /* Instantiate the Animation class. */
           /* The IDs given should match those used in the template above. */
           (function() {
             var img_id = "_anim_img2bee0e98b0754400bc53cc76e7a81e2a";
             var slider_id = "_anim_slider2bee0e98b0754400bc53cc76e7a81e2a";
             var loop_select_id = "_anim_loop_select2bee0e98b0754400bc53cc76e7a81e2a";
             var frames = new Array(250);
    
           frames[0] = "data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfQAAAGQCAYAAABYs5LGAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\
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