Test

Aus Wiki1

Version vom 09:37, 7. Apr. 2023 (Quelltext anzeigen) Emma Lichtenberg (Diskussion | Beiträge) ← Zum vorherigen Versionsunterschied		Aktuelle Version vom 11:23, 5. Sep. 2025 (Quelltext anzeigen) Chantal Schumpeter (Diskussion | Beiträge)
(Der Versionsvergleich bezieht 35 dazwischenliegende Versionen mit ein.)
Zeile 1:		Zeile 1:
-	<painting width=500 height=456>Name der Zeichnung</painting>	+	<jsxgraph box="jxgbox" width="500" height="500">
		+	var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-5,5,5,-5], axis:true});
-	<jsxgraph box="jxgbox" width="500" height="500">	+	// Define the metal plate as a polygon
		+	var polygon = board.create('polygon', [[-4,-4], [-4,4], [4,4], [4,-4]], {fillcolor:'#ddd', hasInnerPoints:true});
		+
		+	// Define the initial temperature distribution as a function of x and y
		+	function initialTemp(x,y) {
		+	return 20 + 10*Math.sin(Math.PI*x/4)*Math.sin(Math.PI*y/4);
		+	}
		+
		+	// Define the temperature function as a function of x and y and time
		+	function temp(x,y,t) {
		+	var k = 1;
		+	var c = 1;
		+	var rho = 1;
		+	var alpha = k/(rho*c);
		+	return initialTemp(x,y) + 10*Math.exp(-alpha*Math.PI*Math.PI*t/16)*Math.sin(Math.PI*x/4)*Math.sin(Math.PI*y/4);
		+	}
		+
		+	// Create a grid of points to sample the temperature function
		+	var points = [];
		+	for (var i=-4; i<=4; i+=0.5) {
		+	for (var j=-4; j<=4; j+=0.5) {
		+	points.push([i,j]);
		+	}
		+	}
		+
		+	// Plot the temperature distribution at time t=0
		+	var heatmap = board.create('polygon', [points, initialTemp], {colorscheme:'greyscale', minopacity:0.5});
		+
		+	// Animate the temperature distribution over time
		+	var time = 0;
		+	var dt = 0.1;
		+	var interval = setInterval(function() {
		+	time += dt;
		+	var values = [];
		+	for (var i=0; i<points.length; i++) {
		+	values.push(temp(points[i][0], points[i][1], time));
		+	}
		+	heatmap.updateData(values);
		+	if (time >= 2) clearInterval(interval);
		+	}, 100);
		+
		+
		+	</jsxgraph>
		+
		+
		+	<jsxgraph box="box" width="500" height="500">
		+
		+	var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-3,3,3,-3], axis:true});
		+
		+	// Parameter
		+	let g = 9.81;
		+	let l1 = 1.0, l2 = 1.0;
		+	let m1 = 1.0, m2 = 1.0;
		+
		+	// Anfangsbedingungen (Winkel in Radiant)
		+	let theta1 = 0.1*Math.PI/2;    // oberes Pendel
		+	let theta2 = 0.1*Math.PI/4;    // unteres Pendel
		+	let omega1 = 0;            // Winkelgeschwindigkeit 1
		+	let omega2 = 0;            // Winkelgeschwindigkeit 2
		+
		+	// Hilfsfunktion: Bewegungsgleichungen (Runge-Kutta 4)
		+	function dOmega(theta1, theta2, omega1, omega2) {
		+	let delta = theta2 - theta1;
		+
		+	let den1 = (m1+m2)*l1 - m2*l1*Math.cos(delta)*Math.cos(delta);
		+	let den2 = (l2/l1)*den1;
		+
		+	let a1 = (m2*l1*omega1*omega1*Math.sin(delta)*Math.cos(delta)
		+	+ m2*g*Math.sin(theta2)*Math.cos(delta)
		+	+ m2*l2*omega2*omega2*Math.sin(delta)
		+	- (m1+m2)*g*Math.sin(theta1)) / den1;
		+
		+	let a2 = (-m2*l2*omega2*omega2*Math.sin(delta)*Math.cos(delta)
		+	+ (m1+m2)*(g*Math.sin(theta1)*Math.cos(delta)
		+	- l1*omega1*omega1*Math.sin(delta)
		+	- g*Math.sin(theta2))) / den2;
		+
		+	return [a1, a2];
		+	}
		+
		+	function rk4(dt) {
		+	let [k1a1, k1a2] = dOmega(theta1, theta2, omega1, omega2);
		+
		+	let t1 = theta1 + 0.5*dt*omega1;
		+	let t2 = theta2 + 0.5*dt*omega2;
		+	let w1 = omega1 + 0.5*dt*k1a1;
		+	let w2 = omega2 + 0.5*dt*k1a2;
		+	let [k2a1, k2a2] = dOmega(t1, t2, w1, w2);
		+
		+	t1 = theta1 + 0.5*dt*omega1;
		+	t2 = theta2 + 0.5*dt*omega2;
		+	w1 = omega1 + 0.5*dt*k2a1;
		+	w2 = omega2 + 0.5*dt*k2a2;
		+	let [k3a1, k3a2] = dOmega(t1, t2, w1, w2);
		+
		+	t1 = theta1 + dt*omega1;
		+	t2 = theta2 + dt*omega2;
		+	w1 = omega1 + dt*k3a1;
		+	w2 = omega2 + dt*k3a2;
		+	let [k4a1, k4a2] = dOmega(t1, t2, w1, w2);
		+
		+	theta1 += dt*(omega1 + (w1 + 2*(omega1 + w1))/6); // kleine Vereinfachung
		+	theta2 += dt*(omega2 + (w2 + 2*(omega2 + w2))/6);
		+
		+	omega1 += dt*(k1a1 + 2*k2a1 + 2*k3a1 + k4a1)/6;
		+	omega2 += dt*(k1a2 + 2*k2a2 + 2*k3a2 + k4a2)/6;
		+	}
		+
		+	// Punkte für das Pendel
		+	let origin = brd.create('point', [0,0], {fixed:true, size:2, name:''});
		+	let p1 = brd.create('point', [
		+	() => l1*Math.sin(theta1),
		+	() => -l1*Math.cos(theta1)
		+	], {size:2, name:'', color:'red'});
		+	let p2 = brd.create('point', [
		+	() => l1*Math.sin(theta1) + l2*Math.sin(theta2),
		+	() => -l1*Math.cos(theta1) - l2*Math.cos(theta2)
		+	], {size:2, name:'', fillColor: 'rgba(255, 0, 0, 0.5)', trace:true});
		+	// Verbindungen
		+	brd.create('line', [origin, p1], {straightFirst:false, straightLast:false});
		+	brd.create('line', [p1, p2], {straightFirst:false, straightLast:false});
-	var board = JXG.JSXGraph.initBoard("jxgbox", {boundingbox: [-2, 8, 12, -2], axis:true});	+	// Animation
-		+	function step() {
-	// Erstelle den linken Wärmetauscher	+	rk4(0.01);
-	var heatexchanger1 = board.create('curve', [[0,0], [3,3], [6,3], [6,6], [3,6], [0,9], [-3,6], [-3,3], [0,0]], {strokeColor:'#00f', fillColor:'#00f', fillOpacity:0.5});	+	brd.update();
-		+	requestAnimationFrame(step);
-	// Erstelle den rechten Wärmetauscher	+	}
-	var heatexchanger2 = board.create('curve', [[8,0], [11,3], [14,3], [14,6], [11,6], [8,9], [5,6], [5,3], [8,0]], {strokeColor:'#f00', fillColor:'#f00', fillOpacity:0.5});	+	step();
-		+
-	// Erstelle die Trennwand	+
-	var wall = board.create('line', [[6,0], [6,9]], {strokeColor:'#000', strokeWidth:4});	+
-		+
-	// Erstelle die Temperaturmesspunkte	+
-	var temp1 = board.create('glider', [2,2,heatexchanger1], {strokeColor:'#00f', fillColor:'#00f', size:10, name:'T1'});	+
-	var temp2 = board.create('glider', [10,2,heatexchanger2], {strokeColor:'#f00', fillColor:'#f00', size:10, name:'T2'});	+
-		+
-	// Berechne die Temperaturdifferenz	+
-	var deltaT = board.create('segment', [temp1, temp2], {strokeColor:'#000', strokeWidth:2});	+
-	var label = board.create('text', [8, 7, function(){return 'ΔT = ' + Math.abs(temp1.Y() - temp2.Y()).toFixed(1) + ' K';}], {fontSize:18});	+
-		+
-	board.update();	+
-		+
	</jsxgraph>		</jsxgraph>

---

Aktuelle Version vom 11:23, 5. Sep. 2025