Mathematics – General Mathematics
Scientific paper
2007-01-26
Mathematics
General Mathematics
5 references; about 2500 words
Scientific paper
The general 4D rotation matrix is specialised to the general 3D rotation matrix by equating its leftmost top element (a00) to 1. Its associate matrix of products of the left-hand and right-hand quaternion components is specialised correspondingly. Inequalities involving the angles through which the coordinate axes in 3D space are displaced are used to prove that the left-hand and the right-hand quaternions are each other's inverses, thus proving the Euler-Rodrigues formula. A general procedure to determine the Euler parameters of a given 3D rotation matrix is sketched. By equating the leftmost top element to -1 instead of +1 in the general 4D rotation matrix, one proves the counterpart of the Euler-Rodrigues formula for 3D rotoreflections. Keywords: Euler--Rodrigues formula, Euler parameters, quaternions, four--dimensional rotations, three--dimensional rotations, rotoreflections
No associations
LandOfFree
Derivation of the Euler-Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Derivation of the Euler-Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Derivation of the Euler-Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-568351