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Use MATLAB to solve the following problems related to rigid motion. Use different colors to display your results.

- Simulate the rigid motion with matrix R and translation o_{\beta'} prescribed by Equation 4.4 in PRO-2014-Lecture.pdf. Basis \beta equals the standard basis \sigma.

% approximate rotation R = [0.8047 -0.5059 -0.3106 0.3106 0.8047 -0.5059 0.5059 0.3106 0.8047];

% less approximate rotation [U,D,V] = svd(R); R = U*V';

% translation o_{\beta'} o = [1;1;1];

- Find the coordinates of vectors of \beta' in \beta and vice versa.
- Plot vectors of \beta and \beta' in the standard basis, list the numeric values.
- Plot coordinate systems (O=0,\beta) and (O',\beta'). i.e. plot the basic vectors as bound vectors originating from points O and O', respectively, list the numeric values.
- Plot the bound vector X_\beta = [1;2;3] representing point X in (0,\sigma), list the numeric values.
- Plot the position vector in (O',\beta') of point Y represented in (O',\beta') by vector Y_{\beta'} = [1;2;3], list the numeric values.
- Consider point Z, where X moves by the motion given above. Plot the bound vector representing the point Z w.r.t. (O=0,\beta), list the numeric values.

Upload via the course ware the zip archive `hw04.zip`

containing

- hw04.pdf report file describing your solution with all figures
- hw04.m MATLAB source code, which generates the results and figures for the report
- all your additional MATLAB files required by hw04.m

courses/pro/labs/hw03.txt · Last modified: 2018/10/09 15:03 by trutmpav