Merge pull request #110 from moorepants/dynamics-overview-exercises

Added exercises to the dynamics overview notebook.

notebooks/exercise_solutions/n01_vector_addition_scaling.py

@@ -0,0 +1,10 @@
+from sympy import sin, cos, pi
+from sympy.abc import l, theta
+
+N = ReferenceFrame('N')
+
+v1 = l * cos(pi / 4) * N.x + l * sin(pi / 4) * N.y
+v2 = -10 * N.y
+v3 = l * cos(theta) * N.x + l * sin(theta) * N.y
+
+v1 + v2 - 5 * v3

notebooks/exercise_solutions/n01_vector_cross_product.py

@@ -0,0 +1,5 @@
+p1 = 23 * N.x - 12 * N.y
+p2 = 16 * N.x + 2 * N.y - 4 * N.z
+p3 = N.x + 14 * N.z
+
+cross(p2 - p1, p3 - p1).magnitude() / 2

notebooks/exercise_solutions/n01_vector_dot_product.py

@@ -0,0 +1,8 @@
+from sympy import acos
+
+N = ReferenceFrame('N')
+
+v1 = a * N.x + b * N.y + a * N.z
+v2 = b * N.x + a * N.y + b * N.z
+
+acos(v1.dot(v2) / (v1.magnitude() * v2.magnitude()))

notebooks/exercise_solutions/n01_vector_rotation.py

@@ -0,0 +1,12 @@
+from sympy import pi
+from sympy.abc import l, w
+
+keyboard_frame = ReferenceFrame('K')
+intermediate_frame = ReferenceFrame('I')
+screen_frame = ReferenceFrame('S')
+
+intermediate_frame.orient(keyboard_frame, 'Axis', (theta, -keyboard_frame.z))
+screen_frame.orient(intermediate_frame, 'Axis', (pi, intermediate_frame.y))
+
+v = l * keyboard_frame.y + w * keyboard_frame.z - l * screen_frame.y
+v.express(keyboard_frame)