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## Homework 05 - Motion Axis

1. 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.
2. Find the axis of motion a_0 for (R,o_\beta'=[0;0;0]) and a_1 for (R,o_\beta'=[1;1;1]).
3. Draw coordinate systems and motion axes.
4. 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.)
5. 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.
6. Consider next only motion (R,o_\beta'=[1;1;1]) and the corresponding a_1.
7. What is the relationship between the generators of \sigma and the matrix (R-I)?
8. Find the point P where motion axis a_1 intersects plane \sigma, and draw it.
9. Find and draw point P', which is obtained by rotating P by rotation R.
10. Find and draw point P' ', which is obtained by translating P' along o'_\beta.
11. What is the relationship between P, P', P' ' and axis a_1?
12. What is the relationship between rotation axis r and motion axis a_1 when:
1. R = I
2. o'_\beta = 0
3. o'_\beta is an eigenvector of R

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