More Properties of SO(3)
These problems will explore in a bit more depth some
properties of rotation matrices
 Solve problem 219. This problem investigates the
meaning of the Eigenvalues and Eigenvectors of a rotation
matrix.
 Solve problem 225. This problem deals with the number
of ways to parameterize a rotation using three angles.
 Solve problem 243. This problem investigates the
commutativity of composition of rotations.
Composition of Rotations
 Solve problems 210, 211, 212, and 213. The problems
will give you practice with the composition of transformations.
 Solve problems 214 and 215.
Axis/Angle Parameterization of SO(3)
 Solve problems 221 and 223.
Complex Number Parameterization of SO(2)
 Solve problems 226 and 227. This problem shows how complex numbers
can be used to represent orientation in the plane.
 Solve problems 228, 229, 230. These problems show how complex
numbers can be generalized to quaternions, and how quaternions
can be used to represent rotations.
 Solve problems 231, 232 and 233. These problems introduce
basic algebraic manipulations of quaternions.
 Solve problems 234 and 235. These problems show how
quaternions can be used to perform coordinate transformations.
