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Paper Abstract and Keywords
Presentation 2021-08-26 15:50
A Quaternion Vector Theory
Osamu Ichiyoshi (HNB21C) SANE2021-26
Abstract (in Japanese) (See Japanese page) 
(in English) In order for the flight control of such flying objects as space rockets or satellites a continuous conversion between the coordinates systems fixed with the fuselage and external inertia space itself. Those flying machines are equipped with coordinate transformation systems that operate based on the data given by acceleration or angular velocity detections systems. The coordinates transformation is made by rotation of a reference vector around the axis vector by amount of the angle given by the above control systems. One of the very beautiful methods of such coordinate transformation is based on the quaternion algebra, which is a complex number system expanded to three dimensions. Is it possible to replace the complex number system with a real vector system? The author has achieved this by defining a quaternion vector product (x) as follows. For vectors u and v, u (x) v = u x v – (u.v), where u x v and (u.v) are respectively normal vector product and scalar product of vectors u and v. The proposed quaternion vector system is essentially equivalent to the quaternion system but formulae can be handled much more easily by use of the vector and scalar products means. For any vector a with a unit length, a (x) a = -1, which is similar to the imaginary number. Thus the formula e^(aθ) = cos(θ) + a.sin(θ) can simplify formulae expressions.
Keyword (in Japanese) (See Japanese page) 
(in English) coordinates / conversion / rotation / vector / quaternion / inertia / fuselage / vector product  
Reference Info. IEICE Tech. Rep., vol. 121, no. 154, SANE2021-26, pp. 22-25, Aug. 2021.
Paper # SANE2021-26 
Date of Issue 2021-08-19 (SANE) 
ISSN Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee SANE  
Conference Date 2021-08-26 - 2021-08-27 
Place (in Japanese) (See Japanese page) 
Place (in English) Online 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Positioning, navigation, Telecommunication, Uninhabited system and general 
Paper Information
Registration To SANE 
Conference Code 2021-08-SANE 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Quaternion Vector Theory 
Sub Title (in English)  
Keyword(1) coordinates  
Keyword(2) conversion  
Keyword(3) rotation  
Keyword(4) vector  
Keyword(5) quaternion  
Keyword(6) inertia  
Keyword(7) fuselage  
Keyword(8) vector product  
1st Author's Name Osamu Ichiyoshi  
1st Author's Affiliation Human Network for Better 21 Century (HNB21C)
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Speaker Author-1 
Date Time 2021-08-26 15:50:00 
Presentation Time 25 minutes 
Registration for SANE 
Paper # SANE2021-26 
Volume (vol) vol.121 
Number (no) no.154 
Page pp.22-25 
#Pages 4 
Date of Issue 2021-08-19 (SANE) 

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