[lesson2] Added challenges.

Author: Murilo M. Marinho

basic_lessons/lesson2_tutorial.ipynb

@@ -662,6 +662,21 @@
     "\n",
     "H_d = None # Replace None with your solution to this exercise."
    ]
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": [
+    "# Extra challenge(s)\n",
+    "1. Let a rotation represented by a SO(2) element have a time-varying angle of $\\theta(t) = \\sin(t) + 2\\cos(t)$.\n",
+    "    - Write down its general form in SO(2) so that all four elements are clearly visible.\n",
+    "    - Using this written down solution, compute the SO(2) representation at $t=10$.\n",
+    "2. Using SO(3) elements, calculate the final rigid body motion after four sequential transformations.\n",
+    "    - The first transformation is a rotation of $\\theta=\\frac{\\pi}{10}$ about the $z$-axis.\n",
+    "    - The second transformation is a translation of $d=0.3$ about the $z$-axis.\n",
+    "    - The third transformation is a translation of $a=0.5$ about the $x$-axis.\n",
+    "    - The forth and last transformation is a rotation of $\\alpha=-\\frac{pi}{2}$ about the $x$-axis."
+   ]
   }
  ],
  "metadata": {