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Pendules
Pendule simple
C = [0,0]
t = 0
a = 0.5
f = 0
w0 = 1
theta = a*cos(w0*t+f)
r = 6
D = [r*sin(theta),-r*cos(theta)]
point(C)
point(D)
segment(C,D)
setInterval(rotation, 50)
function rotation(){
peinture = blanc
transparence = 1
rectangle([-11,11],25,25)
t = t+0.1
theta = a*cos(w0*t+f)
D = [r*sin(theta),-r*cos(theta)]
point(C)
point(D)
segment(C,D)
}
Pendule double
Un seul pendule double
Xmin = 0
Xmax = 700
Ymin = 0
Ymax = 500
var d2Theta1 = 0;
var d2Theta2 = 0;
var dTheta1 = 0;
var dTheta2 = 0;
var Theta1 = 0*(Math.PI)/2;
var Theta2 = 2.3*(Math.PI)/2;
var m1 = 10;
var m2 = 10;
var l1 = 150;
var l2 = 150;
var X0 = 350;
var Y0 = 60;
var g = 9.8;
var time = 0.05;
setInterval(animate, 10)
function animate() {
mu = 1+m1/m2;
d2Theta1 = (g*(sin(Theta2)*cos(Theta1-Theta2)-mu*sin(Theta1))-(l2*dTheta2*dTheta2+l1*dTheta1*dTheta1*cos(Theta1-Theta2))*sin(Theta1-Theta2))/(l1*(mu-cos(Theta1-Theta2)*cos(Theta1-Theta2)));
d2Theta2 = (mu*g*(sin(Theta1)*cos(Theta1-Theta2)-sin(Theta2))+(mu*l1*dTheta1*dTheta1+l2*dTheta2*dTheta2*cos(Theta1-Theta2))*sin(Theta1-Theta2))/(l2*(mu-cos(Theta1-Theta2)*cos(Theta1-Theta2)));
dTheta1 += d2Theta1*time;
dTheta2 += d2Theta2*time;
Theta1 += dTheta1*time;
Theta2 += dTheta2*time;
A = [X0+l1*sin(Theta1), 500-(Y0+l1*cos(Theta1))];
B = [ X0+l1*sin(Theta1)+l2*sin(Theta2), 500-(Y0+l1*cos(Theta1)+l2*cos(Theta2))];
transparence = 1
peinture = blanc
rectangle([-10,800],800,900)
point([350,440])
segment(A,B)
segment([350,440],A)
point(A)
point(B)
}
Xmin = 0
Xmax = 700
Ymin = 0
Ymax = 500
var d2Theta1 = 0;
var d2Theta2 = 0;
var dTheta1 = 0;
var dTheta2 = 0;
var Theta1 = 0*(Math.PI)/2;
var Theta2 = 2.3*(Math.PI)/2;
var m1 = 10;
var m2 = 20;
var l1 = 150;
var l2 = 50;
var X0 = 350;
var Y0 = 60;
var g = 9.8;
var time = 0.05;
setInterval(animate, 10)
function animate() {
mu = 1+m1/m2;
d2Theta1 = (g*(sin(Theta2)*cos(Theta1-Theta2)-mu*sin(Theta1))-(l2*dTheta2*dTheta2+l1*dTheta1*dTheta1*cos(Theta1-Theta2))*sin(Theta1-Theta2))/(l1*(mu-cos(Theta1-Theta2)*cos(Theta1-Theta2)));
d2Theta2 = (mu*g*(sin(Theta1)*cos(Theta1-Theta2)-sin(Theta2))+(mu*l1*dTheta1*dTheta1+l2*dTheta2*dTheta2*cos(Theta1-Theta2))*sin(Theta1-Theta2))/(l2*(mu-cos(Theta1-Theta2)*cos(Theta1-Theta2)));
dTheta1 += d2Theta1*time;
dTheta2 += d2Theta2*time;
Theta1 += dTheta1*time;
Theta2 += dTheta2*time;
A3 = [X0+l1*sin(Theta1), 500-(Y0+l1*cos(Theta1))];
B3 = [ X0+l1*sin(Theta1)+l2*sin(Theta2), 500-(Y0+l1*cos(Theta1)+l2*cos(Theta2))];
transparence = 1
peinture = blanc
rectangle([-10,800],800,900)
point([350,440])
segment(A3,B3)
segment([350,440],A3)
point(A3)
point(B3)
}
Deux pendules doubles avec des conditions initiales proches
Xmin = 0
Xmax = 700
Ymin = 0
Ymax = 500
var d2Theta1 = 0;
var d2Theta2 = 0;
var dTheta1 = 0;
var dTheta2 = 0;
var Theta1 = 0*(Math.PI)/2;
var Theta2 = 2.3*(Math.PI)/2;
var m1 = 10;
var m2 = 10;
var l1 = 150;
var l2 = 150;
var X0 = 350;
var Y0 = 60;
var g = 9.8;
var time = 0.05;
var d2Theta1b = 0;
var d2Theta2b = 0;
var dTheta1b = 0;
var dTheta2b = 0;
var Theta1b = 0*(Math.PI)/2;
var Theta2b = 2.3*(Math.PI)/2;
var m1b = 10;
var m2b = 10.01;
var l1b = 150;
var l2b = 150;
setInterval(animate, 10)
function animate() {
mu = 1+m1/m2;
d2Theta1 = (g*(sin(Theta2)*cos(Theta1-Theta2)-mu*sin(Theta1))-(l2*dTheta2*dTheta2+l1*dTheta1*dTheta1*cos(Theta1-Theta2))*sin(Theta1-Theta2))/(l1*(mu-cos(Theta1-Theta2)*cos(Theta1-Theta2)));
d2Theta2 = (mu*g*(sin(Theta1)*cos(Theta1-Theta2)-sin(Theta2))+(mu*l1*dTheta1*dTheta1+l2*dTheta2*dTheta2*cos(Theta1-Theta2))*sin(Theta1-Theta2))/(l2*(mu-cos(Theta1-Theta2)*cos(Theta1-Theta2)));
dTheta1 += d2Theta1*time;
dTheta2 += d2Theta2*time;
Theta1 += dTheta1*time;
Theta2 += dTheta2*time;
A1 = [X0+l1*sin(Theta1), 500-(Y0+l1*cos(Theta1))];
B1 = [ X0+l1*sin(Theta1)+l2*sin(Theta2), 500-(Y0+l1*cos(Theta1)+l2*cos(Theta2))];
transparence = 1
peinture = blanc
rectangle([-10,800],800,900)
couleur = noir
point([350,440])
segment(A1,B1)
segment([350,440],A1)
point(A1)
point(B1)
mub = 1+m1b/m2b;
d2Theta1b = (g*(sin(Theta2b)*cos(Theta1b-Theta2b)-mub*sin(Theta1b))-(l2b*dTheta2b*dTheta2b+l1b*dTheta1b*dTheta1b*cos(Theta1b-Theta2b))*sin(Theta1b-Theta2b))/(l1b*(mub-cos(Theta1b-Theta2b)*cos(Theta1b-Theta2b)));
d2Theta2b = (mub*g*(sin(Theta1b)*cos(Theta1b-Theta2b)-sin(Theta2b))+(mub*l1b*dTheta1b*dTheta1b+l2b*dTheta2b*dTheta2b*cos(Theta1b-Theta2b))*sin(Theta1b-Theta2b))/(l2b*(mub-cos(Theta1b-Theta2b)*cos(Theta1b-Theta2b)));
dTheta1b += d2Theta1b*time;
dTheta2b += d2Theta2b*time;
Theta1b += dTheta1b*time;
Theta2b += dTheta2b*time;
A1b = [X0+l1b*sin(Theta1b), 500-(Y0+l1b*cos(Theta1b))];
B1b = [ X0+l1b*sin(Theta1b)+l2b*sin(Theta2b), 500-(Y0+l1b*cos(Theta1b)+l2b*cos(Theta2b))];
couleur = rouge
point([350,440])
segment(A1b,B1b)
segment([350,440],A1b)
point(A1b)
point(B1b)
}