update jupyter docs

PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.ipynb

@@ -24,13 +24,19 @@
     "\n",
     "$x(0) = a_0 = x_s$\n",
     "\n",
-    "x_s is a start x position.\n",
+    "$x_s$ is a start x position.\n",
     "\n",
+    "Then, differentiating this equation with t, \n",
     "\n",
+    "$x'(t) = a_1+2a_2t+3a_3t^2+4a_4t^3$\n",
     "\n",
-    "$e^{i\\pi} + 1 = 0$\n",
+    "So, when time is 0,\n",
     "\n",
-    "\n"
+    "$x'(0) = a_1 = v_s$\n",
+    "\n",
+    "$v_s$ is a initial speed for x axis.\n",
+    "\n",
+    "=== TBD ==== \n"
    ],
    "metadata": {
     "collapsed": false

PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py

@@ -26,6 +26,7 @@ class QuinticPolynomial:
 
     def __init__(self, xs, vxs, axs, xe, vxe, axe, time):
         # calc coefficient of quintic polynomial
+        # See jupyter notebook document for derivation of this equation.
         self.a0 = xs
         self.a1 = vxs
         self.a2 = axs / 2.0