Fork Code: Damped Driven Double Pendulum Sonification and Visualization

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///////////////////////
// Variable declaration
///////////////////////

var centerx = 410, centery = 410, //Coordinates used to offset the pendulum fixed point
r1 = 200, //Length of pendulum rod 1
r2 = 200, //Length of pendulum rod 2
m1 = 20, //Mass of pendulum bob 1
m2 = 20, //Mass of pendulum bob 2
a1 = pi+(rrand(0.0001,0.0009)), //Initial angle of pendulum 1
a2 = pi, //Initial angle of pendulum 2
a1_v = 0, //Initial velocity of pendulum 1
a2_v = 0, //Initial velocity of pendulum 2
g = 1.0, //Gravitational constant

time_step = 1.0,
time = 0,
k1 = 10.0, //Damping coefficient of pendulum 1
k2 = 10.0, //Damping coefficient of pendulum 2, usually same as pendulum 1
force1 = 0.0, //Magnitude of oscillation strength
force2 = 0.0, //This is usually kept at 0
//freq1 = sqrt(g/r1)*sqrt(2+sqrt(2))/100,
freq1 = 0.0, //Drive frequency for pendulum 1
freq2 = 0.0, //Drive frequency for pendulum 2
iterations = 0, //Total frames drawn
alpha, beta, deltheta, num1, num2, num3, num4, gamma, den, //mathematical functions
a1_a, a2_a,  // accelerations
x1, y1, x2, y2, // positions

pitch = 440,

///////////////////////
// Window setup
///////////////////////


width = 820, height = 820,
w = Window("Double Pendulum", Rect(99, 99, width, height), false),
u = UserView(w, Rect(0, 0, width, height));

u.clearOnRefresh = true;
u.background = Color.white;
w.front;
u.frameRate = 40;
u.animate = true;
CmdPeriod.doOnce({if(w.isClosed.not, {w.close})});




///////////////////////
// Synthdef(s)
///////////////////////


SynthDef(\gliss, {
	arg freq=440, gate=1, amp=0.0, out=0;
	var sig, env;
	freq = Lag.kr(freq, 1);
	amp = Lag.kr(amp, 1);
	env = EnvGen.kr(Env.asr, gate, doneAction:2);
	sig = SinOsc.ar(freq)!2;
	sig = sig * amp;
	sig = sig * env;
	Out.ar(out, sig);
}).add;


x = Synth(\gliss);

u.drawFunc = {




	///////////////////////
	// Equations
	///////////////////////

	alpha = (k1 * a1_v) - (force1 * cosPi(freq1 * time));
	beta = (k2 * a2_v) - (force2 * cosPi(freq2 * time));
	deltheta = a1-a2;

	num1 = m2 * r1 * a1_v * a1_v * sinPi(2 * deltheta);
	num2 = 2 * m2 * r2 * a2_v * a2_v * sinPi(deltheta);
	num3 = 2 * g * m2 * cosPi(a2)*sinPi(deltheta);
	num4 = 2 * g * m1 * sinPi(a1);
	gamma = (2*alpha) - (2*beta*cosPi(deltheta));
	den = (-2 * r1*m1) + (r1*m2*sinPi(deltheta)*sinPi(deltheta));
	a1_a = (num1 + num2 + num3 + num4 + gamma)/den;

	num1 = m2 * r2 * a2_v * a2_v * sinPi(2 * deltheta);
	num2 = 2 * (m1+m2) * r1 * a1_v*a1_v * sinPi(deltheta);
	num3 = 2 * g * (m1+m2) * cosPi(a1)*sinPi(deltheta);
	gamma = (2*alpha*cosPi(deltheta)) - (2*(m1+m2)*beta/m2);
	den = (2 * r2*m1) + (r2*m2*sinPi(deltheta)*sinPi(deltheta));
	a2_a = (num1 + num2 + num3 + gamma)/den;

	x1 = r1 * sinPi(a1);
	y1 = r1 * cosPi(a1);

	x2 = x1 + (r2 * sinPi(a2));
	y2 = y1 + (r2 * cosPi(a2));



	///////////////////////
	// Advance position
	///////////////////////

	a1_v = a1_v + a1_a;
	a2_v = a2_v + a2_a;
	a1 = a1 + a1_v;
	a2 = a2 + a2_v;


	///////////////////////
	// Create Window and draw pendulum
	///////////////////////


	Pen.strokeColor = Color.blue;
	Pen.width = 2;
	Pen.moveTo(centerx@centery);
	Pen.lineTo((centerx+x1)@(centery+y1));
	Pen.lineTo((centerx+x2)@(centery+y2));
	Pen.stroke;
	Pen.strokeOval(Rect(centerx+x1-5, centery+y1-5, 10, 10));
	Pen.strokeOval(Rect(centerx+x2-5, centery+y2-5, 10, 10));

	pitch = sqrt((x2*x2)+(y2*y2));

	x.set(\freq, pitch);
	x.set(\amp, a2_v*5);

	time = time + time_step;

	iterations = iterations + 1;
};

)

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