Rigid Body Motions
Rotations and homogeneous transformations are examples of rigid body motions,
i.e., motions that preserve distance and angles. The first questions
explore this topic.
Solve problems 2-1, 2-2 and 2-3. These problems demonstrate
a few properties of rigid body transformations.
Properties of Rotation Matrices
These problems will explore in a bit more depth some
properties of rotation matrices
- Solve problems 2-4 and 2-5.
These problems investigate properties of the Special Orthogonal group of matrices.
You may restrict your attention to SO(3) for these problems (if that makes things
simpler to express).
- Solve problem 2-6. This problem merely demonstrates the intuitive
fact that successive rotations about a single access can be expressed in terms
of the sum of the two angular rotations.
- Solve problem 2-7. This problem establishes
that SO(n) is a group.
- Solve problems 2-38, 2-39, 2-40 and 2-41. These problems illustrate the assignment
of coordinate frames in 3D, and the use of homogeneous transformations.