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===== Homework 05 - Motion Axis =====

=== Task ===

  - 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 ===

Upload via the [[https://cw.felk.cvut.cz/upload/|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).