--> Pendules 1Pendule simple

2Pendule double 2.1Un seul pendule double

Xmin = 0
Xmax = 700
Ymin = 0
Ymax = 700
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 = 700
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)

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)
}

2.2Deux pendules doubles avec des conditions initiales proches

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)

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)
}