WreckingBall.js

var calcPen = function(zLen){
    //Pendulum Movement Equation
    //T = 2pi*SQRT(L/g)
    var twoPi = 6.2831926
    var gravity = 9.8
    var result = twoPi * Math.sqrt(zLen / gravity);
    return(result.toFixed(4))
}

exports.calcVelocity = function(xyLen, jerk, zLen){
  // V = 1 / 3 (3T j v_1 - 3D j - v_1 sqrt(j v_1) sqrt(sqrt(3) 30)) / j
  // V' =  1 / 3 (-sqrt(j v_1) sqrt(sqrt(3) 30) - 1 / 2 j v_1 sqrt(sqrt(3) 30) / sqrt(j v_1) + 3T j) / j
 
    
  var jerk = jerk*1000000;
  var pendulumPeriod = calcPen(zLen/100);
  var sqrt_three_thirty = Math.sqrt(Math.sqrt(3)*30);
 
  // Guess xyLen/pendulumPeriod, which will get the loop started
  var v_1 = xyLen/pendulumPeriod;
 
  // The previous guess -- lets start it way off
  var v_1_previous = v_1-100;
  console.log("v_1: "+ v_1);
 
  while (Math.abs(v_1 - v_1_previous) > VELOCITY_ACCURACY) {
    v_1_previous = v_1;
 
    // V = (3*T*j*v_1 - 3*D*j - v_1*sqrt(j*v_1)*sqrt_three_thirty) / 3*j
    // V' =  (-sqrt(j*v_1)*sqrt_three_thirty - (j*v_1*sqrt_three_thirty)/(2*sqrt(j*v_1)) + 3*T*j) / 3*j
    var sqrt_j_v = Math.sqrt(jerk*v_1);
 
    // V = (3*T*j*v_1 - 3*D*j - v_1*sqrt_j_v*sqrt_three_thirty) / 3*j
    // V' =  (-sqrt_j_v*sqrt_three_thirty - (j*v_1*sqrt_three_thirty)/(2*sqrt_j_v) + 3*T*j) / 3*j
 
    var F_v_1 = (3*pendulumPeriod*jerk*v_1 - 3*xyLen*jerk - v_1*sqrt_j_v*sqrt_three_thirty) / 3*jerk;
    var Fd_v_1 = (-sqrt_j_v*sqrt_three_thirty - (jerk*v_1*sqrt_three_thirty)/(2*sqrt_j_v) + 3*pendulumPeriod*jerk) / 3*jerk;
 
    v_1 = v_1 - (F_v_1/Fd_v_1);
    console.log("v_1: "+ v_1.toFixed(4) + " F_v_1: " + F_v_1.toFixed(4) + " Fd_v_1: " + Fd_v_1.toFixed(4));
  }
 
  return v_1*60;
}