Paper Info
Title
New Formulae To Approximate An Infinitesimal Rotation Followed Or Preceded By A Large One
Abstract
Rotations of the Cartesian reference frames are used extensively in many fields of research such as navigation and guidance systems, and motion tracking systems. Of particular interest is the case when an infinitesimal rotation is followed or preceded by a large rotation. If the order of rotations is required to be changed, there is no formula to describe a good approximation. Instead, researchers usually use dot product of the unit vectors of the coordinate systems before and after the reversal. In this work, we provide a direct formula for such approximation. Further, we show that the proposed formulae can be used to construct the inverse of any transformation comprising two successive rotations about different axes by taking many successive infinitesimal rotations approximated properly. Moreover, we present a case study for which the proposed formulae can be used to find the solution in a direct way compared to other techniques.
Year
DOI
Venue
2018
10.23919/ECC.2018.8550116
2018 EUROPEAN CONTROL CONFERENCE (ECC)
Field
DocType
Citations 
Coordinate system,Infinitesimal transformation,Reference frame,Mathematical analysis,Dot product,Infinitesimal,Match moving,Mathematics,Cartesian coordinate system,Unit vector
Conference
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Mutaz Tuffaha100.68
Øyvind Stavdahl212515.09
Ann-Katrin Stensdotter300.68