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 triangular. 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, 24 69...
View
Full Document
 Fall '11
 Dr.Robin
 Matrices, Singular value decomposition, Orthogonal matrix, Qroll Qpitch Qyaw

Click to edit the document details