More Properties of SO(3)
These problems will explore in a bit more depth some
properties of rotation matrices
- Solve problem 2-19. This problem investigates the
meaning of the Eigenvalues and Eigenvectors of a rotation
- Solve problem 2-25. This problem deals with the number
of ways to parameterize a rotation using three angles.
- Solve problem 2-43. This problem investigates the
commutativity of composition of rotations.
Composition of Rotations
- Solve problems 2-10, 2-11, 2-12, and 2-13. The problems
will give you practice with the composition of transformations.
- Solve problems 2-14 and 2-15.
Axis/Angle Parameterization of SO(3)
- Solve problems 2-21 and 2-23.
Complex Number Parameterization of SO(2)
- Solve problems 2-26 and 2-27. This problem shows how complex numbers
can be used to represent orientation in the plane.
- Solve problems 2-28, 2-29, 2-30. These problems show how complex
numbers can be generalized to quaternions, and how quaternions
can be used to represent rotations.
- Solve problems 2-31, 2-32 and 2-33. These problems introduce
basic algebraic manipulations of quaternions.
- Solve problems 2-34 and 2-35. These problems show how
quaternions can be used to perform coordinate transformations.