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- Consider the same motion as in HW-04. Draw figures in a similar way as in HW-04. Give numerical values for all vectors and matrices.
- Find the axis of motion a_0 for (R,o_\beta'=[0;0;0]) and a_1 for (R,o_\beta'=[1;1;1]).
- Draw coordinate systems and motion axes.
- Find and draw rotation axes r. What is the relationship beween r, a_0, and a_1 (Use equaiton (R-I)^2*x_\beta = -(R-I)*o'_\beta.)
- Find the plane \sigma, which is perpendicular to rotation axis r, some set of its generators (i.e. vectors that generate it) and draw them into the figure.
- Consider next only motion (R,o_\beta'=[1;1;1]) and the corresponding a_1.
- What is the relationship between the generators of \sigma and the matrix (R-I)?
- Find the point P where motion axis a_1 intersects plane \sigma, and draw it.
- Find and draw point P', which is obtained by rotating P by rotation R.
- Find and draw point P' ', which is obtained by translating P' along o'_\beta.
- What is the relationship between P, P', P' ' and axis a_1?
- What is the relationship between rotation axis r and motion axis a_1 when:
- R = I
- o'_\beta = 0
- o'_\beta is an eigenvector of R

Upload via the course ware the zip archive `hw05.zip`

containing

- hw05.m Matlab script (functions) solving the assignment.
- hw05.pdf description of the solution (algotihms, results, comments).

courses/pro/labs/hw05.txt · Last modified: 2018/10/29 12:31 by policmic