Unformatted text preview: θ and sin θ to compensate.) Finally, we can choose ψ to ±orce Q roll Q pitch Q yaw Q T to be upper tri-angular. Since the product o± orthogonal matrices is orthogonal, and the only upper triangular orthogonal matrices are diagonal, we conclude that Q roll Q pitch Q yaw is a diagonal matrix (with entries ± 1) times ( Q T ) − 1 . Now convince yoursel± that the angles can be chosen so that the diagonal matrix is the identity. This method ±or proving this property is particularly nice because it leads to a ±ast algorithm that we can use in Challenge 4 to recover the Euler angles given an orthogonal matrix Q . CHALLENGE 12.2. A sample MATLAB program to solve this problem is available on the website. The results are shown in Figure 12.1. In most cases, 2-4 69...
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- Fall '11
- Matrices, Singular value decomposition, Orthogonal matrix, Qroll Qpitch Qyaw