*Problem 12 - 10 points Any 3D rotation R around 0 is characterized by three angles: the yaw 0, the pitch and the roll p

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Problem 12 10 Points Any 3d Rotation R Around 0 Is Characterized By Three Angles The Yaw 0 The Pitch And The Roll P 1 (68.09 KiB) Viewed 126 times

*Problem 12 - 10 points Any 3D rotation R around 0 is characterized by three angles: the yaw 0, the pitch and the roll p, in the following way: if • RZe is the counter-clockwise rotation of angle around the z axis, • RY is the counter-clockwise rotation of angle o around the y axis, • RX, is the counter-clockwise rotation of angle p around the z axis, then R = RX₂0 RY, RZ, is the rotation of yaw 0, pitch and roll p. The corresponding rotation matrices are given by: Rr(p) = [10 0 0 cos p sin p Ry(o)= [0 sin p cos p - [coso 0-sin 0 1 0 sino 0 cos R₂(0) cos sin 0 sin 0 0 cos 0 0 0 1 We also have Euler's Rotation Theorem which says that for any 3D rotation around 0 there exists an invariant aris U, i.e., a subspace of dimension 1 of vectors that are left invariant by the rotation meaning V EU, R(v) = 0. In this problem, you will write a MATLAB function that be given the three angles (0.0, p) of a 3D rotation around 0 returns a basis for the invariant axis U. A. Let (0.0, p) be the three angles of a 3D rotation around 0. Write a MATLAB function called matrixFromAngles that returns the matrix of this rotation. (3) B. Let R be the matrix of a 3D rotation around 0. Write the matrix form of the system of linear equations satisfied by any vector in the invariant axis. (2) C. Write a MATLAB function called axisFromThreeAngles taking in input the three angles 0, 0, p characterizing a rotation, and returning a basis for the invariant axis U. (2) D. Compute the invariant axis of the rotation of yaw 8/2, pitch = 1/3 and roll p = x/4. (3) hint: the MATLAB function null returns a basis for the nullspace of a matrix.