diff --git a/06-pendulum.html b/06-pendulum.html
new file mode 100644
index 0000000..a7b9039
--- /dev/null
+++ b/06-pendulum.html
@@ -0,0 +1,356 @@
+<!--
+Copyright 2021 Matthias Müller - Ten Minute Physics
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+-->
+
+<!DOCTYPE html>
+<html>
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>Pendulum</title>
+<style>
+    body {
+        font-family: verdana; 
+        font-size: 15px;
+    }			
+    .button {
+    background-color: #606060;
+    border: none;
+    color: white;
+    padding: 15px 32px;
+    font-size: 16px;
+    margin: 4px 2px;
+    cursor: pointer;
+}
+</style>
+
+<body>
+	<button class="button" onclick="setupScene()">Restart</button>
+	<button class="button" onclick="run()">Run</button>
+	<button class="button" onclick="step()">Step</button>
+    <p>Number of sub-steps: <input type = "range" min = "0" max = "5" value = "5" id = "stepsSlider" class = "slider"> <span id = "steps">10000</span></p>
+
+	<canvas id = "myCanvas"></canvas>
+<script>
+   	var canvas = document.getElementById("myCanvas");
+	var c = canvas.getContext("2d");
+	canvas.width = window.innerWidth - 20;
+	canvas.height = window.innerHeight - 20;
+
+	var simMinWidth = 1.0;
+	var cScale = Math.min(canvas.width, canvas.height) / simMinWidth;
+
+	function cX(pos) { return canvas.width / 2 + pos.x * cScale; }
+	function cY(pos) { return 0.4 * canvas.height - pos.y * cScale; }
+
+    class Pendulum {
+        constructor(usePBD, color, masses, lengths, angles) {
+            this.usePBD = usePBD;
+            this.color = color;
+            this.masses = [0.0];
+            this.lengths = [0.0];
+            this.pos = [{x:0.0, y:0.0}];
+            this.prevPos = [{x:0.0, y:0.0}];
+            this.vel = [{x:0.0, y:0.0}];
+            this.theta = [0.0];
+            this.omega = [0.0];
+
+            this.trail = new Int32Array(1000);
+            this.trailFirst = 0;
+            this.trailLast = 0;
+
+            var x = 0.0, y = 0.0;
+            for (var i = 0; i < masses.length; i++) {
+                this.masses.push(masses[i]);
+                this.lengths.push(lengths[i]);
+                this.theta.push(angles[i]);
+                this.omega.push(0.0);
+                x += lengths[i] * Math.sin(angles[i]);
+                y += lengths[i] * -Math.cos(angles[i]); 
+                this.pos.push({ x:x, y:y});
+                this.prevPos.push({ x:x, y:y});
+                this.vel.push({x:0, y:0});
+            }
+        }
+        simulate(dt, gravity) {
+            if (this.usePBD)
+                this.simulatePBD(dt, gravity);
+            else
+                this.simulateAnalytic(dt, gravity);
+        }
+        simulatePBD(dt, gravity) 
+        {
+            var p = this;
+            for (var i = 1; i < p.masses.length; i++) {
+                p.vel[i].y += dt * scene.gravity;
+                p.prevPos[i].x = p.pos[i].x;
+                p.prevPos[i].y = p.pos[i].y;
+                p.pos[i].x += p.vel[i].x * dt;
+                p.pos[i].y += p.vel[i].y * dt;
+            }
+            for (var i = 1; i < p.masses.length; i++) {
+                var dx = p.pos[i].x - p.pos[i-1].x;
+                var dy = p.pos[i].y - p.pos[i-1].y;
+                var d = Math.sqrt(dx * dx + dy * dy);
+                var w0 = p.masses[i - 1] > 0.0 ? 1.0 / p.masses[i - 1] : 0.0;
+                var w1 = p.masses[i] > 0.0 ? 1.0 / p.masses[i] : 0.0;
+                var corr = (p.lengths[i] - d) / d / (w0 + w1);
+                p.pos[i - 1].x -= w0 * corr * dx; 
+                p.pos[i - 1].y -= w0 * corr * dy; 
+                p.pos[i].x += w1 * corr * dx; 
+                p.pos[i].y += w1 * corr * dy; 
+            }
+            for (var i = 1; i < p.masses.length; i++) {
+                p.vel[i].x = (p.pos[i].x - p.prevPos[i].x) / dt;
+                p.vel[i].y = (p.pos[i].y - p.prevPos[i].y) / dt;
+            }
+        }
+        simulateAnalytic(dt, gravity) 
+        {
+			var g = -gravity;
+			var m1 = this.masses[1];
+			var m2 = this.masses[2];
+			var m3 = this.masses[3];
+			var l1 = this.lengths[1];
+			var l2 = this.lengths[2];
+			var l3 = this.lengths[3];
+			var t1 = this.theta[1];
+			var t2 = this.theta[2];
+			var t3 = this.theta[3];
+			var w1 = this.omega[1];
+			var w2 = this.omega[2];
+			var w3 = this.omega[3];
+
+			var b1 = 
+				g*l1*m1*Math.sin(t1) + g*l1*m2*Math.sin(t1)+g*l1*m3*Math.sin(t1) + m2*l1*l2*Math.sin(t1-t2)*w1*w2 + 
+				m3*l1*l3*Math.sin(t1-t3)*w1*w3       +   m3*l1*l2*Math.sin(t1-t2)*w1*w2  +  
+				m2*l1*l2*Math.sin(t2-t1)*(w1-w2)*w2  +   
+				m3*l1*l2*Math.sin(t2-t1)*(w1-w2)*w2  +  
+				m3*l1*l3*Math.sin(t3-t1)*(w1-w3)*w3;
+
+			var a11 = l1*l1*(m1+m2+m3);
+			var a12 = m2*l1*l2*Math.cos(t1-t2) + m3*l1*l2*Math.cos(t1-t2);
+			var a13 = m3*l1*l3*Math.cos(t1-t3);
+
+			var b2 = 
+				g*l2*m2*Math.sin(t2) + g*l2*m3*Math.sin(t2) + w1*w2*l1*l2*Math.sin(t2-t1)*(m2 + m3) +
+				m3*l2*l3*Math.sin(t2-t3)*w2*w3               +    
+				(m2 + m3)*l1*l2*Math.sin(t2-t1)*(w1-w2)*w1   +  
+				m3*l2*l3*Math.sin(t3-t2)*(w2-w3)*w3; 
+
+			var a21 = (m2 + m3)*l1*l2*Math.cos(t2-t1);
+			var a22 = l2*l2*(m2+m3);
+			var a23 = m3*l2*l3*Math.cos(t2-t3);
+
+			var b3 = 
+				m3*g*l3*Math.sin(t3) - m3*l2*l3*Math.sin(t2-t3)*w2*w3 - m3*l1*l3*Math.sin(t1-t3)*w1*w3 + 
+				m3*l1*l3*Math.sin(t3-t1)*(w1-w3)*w1    + 
+				m3*l2*l3*Math.sin(t3-t2)*(w2-w3)*w2;
+
+			var a31 = m3*l1*l3*Math.cos(t1-t3);
+			var a32 = m3*l2*l3*Math.cos(t2-t3);
+			var a33 = m3*l3*l3;
+
+			b1 = -b1;
+			b2 = -b2;
+			b3 = -b3;
+
+			var det = a11 * (a22 * a33 - a23 * a32) + a21 * (a32 * a13 - a33 * a12) + a31 * (a12 * a23 - a13 * a22);
+			if (det == 0.0)
+				return;
+
+			var a1 = b1 * (a22 * a33 - a23 * a32) + b2 * (a32 * a13 - a33 * a12) + b3 * (a12 * a23 - a13 * a22);
+			var a2 = b1 * (a23 * a31 - a21 * a33) + b2 * (a33 * a11 - a31 * a13) + b3 * (a13 * a21 - a11 * a23);
+			var a3 = b1 * (a21 * a32 - a22 * a31) + b2 * (a31 * a12 - a32 * a11) + b3 * (a11 * a22 - a12 * a21);
+
+			a1 /= det;
+			a2 /= det;
+			a3 /= det;
+
+			this.omega[1] += a1 * dt;
+			this.omega[2] += a2 * dt;
+			this.omega[3] += a3 * dt;
+			this.theta[1] += this.omega[1] * dt;
+			this.theta[2] += this.omega[2] * dt;	
+			this.theta[3] += this.omega[3] * dt;	
+
+            var x = 0.0, y = 0.0;
+            for (var i = 1; i < this.masses.length; i++) {
+                x += this.lengths[i] * Math.sin(this.theta[i]);
+                y += this.lengths[i] * -Math.cos(this.theta[i]); 
+                this.pos[i].x = x;
+                this.pos[i].y = y;
+            }
+        }
+        updateTrail() {
+            this.trail[this.trailLast] = cX(this.pos[this.pos.length-1]);
+            this.trail[this.trailLast + 1] = cY(this.pos[this.pos.length-1]);
+            this.trailLast = (this.trailLast + 2) % this.trail.length;
+            if (this.trailLast == this.trailFirst)
+                this.trailFirst = (this.trailFirst + 2) % this.trail.length;
+        }
+        draw() {
+            c.strokeStyle = this.color;
+            c.lineWidth = 2.0;
+            if (this.trailLast != this.trailFirst) {
+                var i = this.trailFirst;
+                c.beginPath();
+                c.moveTo(this.trail[i], this.trail[i + 1]);
+                i = (i + 2) % this.trail.length;
+                while (i != this.trailLast) {
+                    c.lineTo(this.trail[i], this.trail[i + 1]);
+                    i = (i + 2) % this.trail.length;
+                }
+                c.stroke();
+            }
+
+            var p = this;
+            c.strokeStyle = "#303030";
+            c.lineWidth = 10;
+            c.beginPath();
+            c.moveTo(cX(p.pos[0]), cY(p.pos[0]));
+            for (var i = 1; i < p.masses.length; i++) 
+                c.lineTo(cX(p.pos[i]), cY(p.pos[i]));
+            c.stroke();
+            c.lineWidth = 1;            
+
+            c.fillStyle = this.color;
+            for (var i = 1; i < p.masses.length; i++) {
+                var r = 0.03 * Math.sqrt(p.masses[i]);
+                c.beginPath();			
+                c.arc(
+                    cX(p.pos[i]), cY(p.pos[i]), cScale * r, 0.0, 2.0 * Math.PI); 
+                c.closePath();
+                c.fill();
+            }
+        }
+    }
+
+    var scene = {
+        gravity : -10.0,
+        dt : 0.01,
+        numSubSteps : 10000,
+        paused : true,
+        pendulumPBD : null,
+        pendulumAnalytic : null
+    };
+
+    var sceneNr = 0;
+
+    function setupScene() {
+        var angles = [0.5 * Math.PI, Math.PI, Math.PI, Math.PI, Math.PI];
+        var lengths = [];
+        var masses = [];
+
+        switch(sceneNr % 6) {
+            case 0 : {
+                lengths = [0.15, 0.15, 0.15];
+                masses = [1.0, 1.0, 1.0];
+                break;
+            }
+            case 1 : {
+                lengths = [0.06, 0.15, 0.2];
+                masses = [1.0, 0.5, 0.1];
+                break;
+            }
+            case 2 : {
+                lengths = [0.15, 0.15, 0.15];
+                masses = [1.0, 0.01, 1.0];
+                break;
+            }
+            case 3 : {
+                lengths = [0.15, 0.15, 0.15];
+                masses = [0.01, 1.0, 0.01];
+                break;
+            }
+            case 4 : {
+                lengths = [0.2, 0.133, 0.04];
+                masses = [0.3, 0.3, 0.3];
+                break;
+            }
+            case 5 : {
+                lengths = [0.1, 0.12, 0.1, 0.15, 0.05];
+                masses = [0.2, 0.6, 0.4, 0.3, 0.2];
+                break;
+            }
+        }
+
+        scene.pendulumAnalytic = null;
+
+        scene.pendulumPBD = new Pendulum(true, "#FF3030", masses, lengths, angles);
+        if (masses.length <= 3)
+            scene.pendulumAnalytic = new Pendulum(false, "#00FF00", masses, lengths, angles);
+        scene.paused = true;
+
+        sceneNr++;
+    }
+
+    function draw() {
+        c.fillStyle = "#000000";
+        c.fillRect(0, 0, canvas.width, canvas.height);
+        if (scene.pendulumPBD)
+            scene.pendulumPBD.draw();
+        if (scene.numSubSteps >= 100) {
+            if (scene.pendulumAnalytic)
+                scene.pendulumAnalytic.draw();
+        }
+    }
+
+    function simulate() {
+        if (scene.paused)
+            return;
+        var sdt = scene.dt / scene.numSubSteps;
+        var trailGap = scene.numSubSteps / 10;
+
+        for (var step = 0; step < scene.numSubSteps; step++) {
+            if (scene.pendulumPBD) {
+                scene.pendulumPBD.simulate(sdt, scene.gravity);
+                if (step % trailGap == 0)
+                    scene.pendulumPBD.updateTrail();
+            }
+            if (scene.pendulumAnalytic) {
+                scene.pendulumAnalytic.simulate(sdt, scene.gravity);
+                if (step % trailGap == 0)
+                    scene.pendulumAnalytic.updateTrail();
+            }
+        }
+    }
+    
+	document.getElementById("stepsSlider").oninput = function() {
+		var steps = [1, 5, 10, 100, 1000, 10000];
+		scene.numSubSteps = steps[Number(this.value)];
+		document.getElementById("steps").innerHTML = scene.numSubSteps.toString();
+	}
+
+    document.addEventListener("keydown", event => {
+        if (event.isComposing || event.keyCode === 229) 
+            return;
+        if (event.key == 's')
+            step();
+        });    
+
+	function run() {
+		scene.paused = false;
+	}
+
+	function step() {
+		scene.paused = false;
+		simulate();
+		scene.paused = true;
+	}
+
+	function update() {
+		simulate();
+		draw();
+		requestAnimationFrame(update);
+	}
+    setupScene();
+	update();	
+
+</script> 
+</body>
+</html>
\ No newline at end of file
diff --git a/06-pendulumShort.html b/06-pendulumShort.html
new file mode 100644
index 0000000..8f827ff
--- /dev/null
+++ b/06-pendulumShort.html
@@ -0,0 +1,126 @@
+<!--
+Copyright 2021 Matthias Müller - Ten Minute Physics
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+-->
+
+<!DOCTYPE html>
+<html>
+<body>
+	<canvas id = "myCanvas"></canvas>
+<script>
+    var lengths = [0.2, 0.2, 0.2];
+    var masses = [1.0, 0.5, 0.3];
+    var angles = [0.5 * Math.PI, Math.PI, Math.PI];
+
+    var canvas = document.getElementById("myCanvas");
+	var c = canvas.getContext("2d");
+	canvas.width = window.innerWidth - 20;
+	canvas.height = window.innerHeight - 20;
+	var simMinWidth = 1.0;
+	var cScale = Math.min(canvas.width, canvas.height) / simMinWidth;
+
+	function cX(pos) { return canvas.width / 2 + pos.x * cScale; }
+	function cY(pos) { return 0.4 * canvas.height - pos.y * cScale; }
+
+    class Pendulum {
+        constructor(masses, lengths, angles) {
+            this.masses = [0.0];
+            this.lengths = [0.0];
+            this.pos = [{x:0.0, y:0.0}];
+            this.prevPos = [{x:0.0, y:0.0}];
+            this.vel = [{x:0.0, y:0.0}];
+            var x = 0.0, y = 0.0;
+            for (var i = 0; i < masses.length; i++) {
+                this.masses.push(masses[i]);
+                this.lengths.push(lengths[i]);
+                x += lengths[i] * Math.sin(angles[i]);
+                y += lengths[i] * -Math.cos(angles[i]); 
+                this.pos.push({ x:x, y:y});
+                this.prevPos.push({ x:x, y:y});
+                this.vel.push({x:0, y:0});
+            }
+        }
+        simulate(dt, gravity) 
+        {
+            var p = this;
+            for (var i = 1; i < p.masses.length; i++) {
+                p.vel[i].y += dt * scene.gravity;
+                p.prevPos[i].x = p.pos[i].x;
+                p.prevPos[i].y = p.pos[i].y;
+                p.pos[i].x += p.vel[i].x * dt;
+                p.pos[i].y += p.vel[i].y * dt;
+            }
+            for (var i = 1; i < p.masses.length; i++) {
+                var dx = p.pos[i].x - p.pos[i-1].x;
+                var dy = p.pos[i].y - p.pos[i-1].y;
+                var d = Math.sqrt(dx * dx + dy * dy);
+                var w0 = p.masses[i - 1] > 0.0 ? 1.0 / p.masses[i - 1] : 0.0;
+                var w1 = p.masses[i] > 0.0 ? 1.0 / p.masses[i] : 0.0;
+                var corr = (p.lengths[i] - d) / d / (w0 + w1);
+                p.pos[i - 1].x -= w0 * corr * dx; 
+                p.pos[i - 1].y -= w0 * corr * dy; 
+                p.pos[i].x += w1 * corr * dx; 
+                p.pos[i].y += w1 * corr * dy; 
+            }
+            for (var i = 1; i < p.masses.length; i++) {
+                p.vel[i].x = (p.pos[i].x - p.prevPos[i].x) / dt;
+                p.vel[i].y = (p.pos[i].y - p.prevPos[i].y) / dt;
+            }
+        }
+        draw() {
+            var p = this;
+            c.strokeStyle = "#303030";
+            c.lineWidth = 10;
+            c.beginPath();
+            c.moveTo(cX(p.pos[0]), cY(p.pos[0]));
+            for (var i = 1; i < p.masses.length; i++) 
+                c.lineTo(cX(p.pos[i]), cY(p.pos[i]));
+            c.stroke();
+            c.lineWidth = 1;            
+
+            c.fillStyle = "#FF0000";
+            for (var i = 1; i < p.masses.length; i++) {
+                var r = 0.05 * Math.sqrt(p.masses[i]);
+                c.beginPath();			
+                c.arc(
+                    cX(p.pos[i]), cY(p.pos[i]), cScale * r, 0.0, 2.0 * Math.PI); 
+                c.closePath();
+                c.fill();
+            }
+        }
+    }
+
+    var scene = {
+        gravity : -10.0,
+        dt : 0.01,
+        numSubSteps : 100,
+        pendulum : new Pendulum(masses, lengths, angles)
+    };
+
+    function draw() {
+        c.fillStyle = "#000000";
+        c.fillRect(0, 0, canvas.width, canvas.height);
+        scene.pendulum.draw();
+    }
+
+    function simulate() {
+        var sdt = scene.dt / scene.numSubSteps;
+        for (var step = 0; step < scene.numSubSteps; step++) 
+            scene.pendulum.simulate(sdt, scene.gravity);
+    }
+
+	function update() {
+		simulate();
+		draw();
+		requestAnimationFrame(update);
+	}
+	
+	update();	
+</script> 
+</body>
+</html>
\ No newline at end of file
