NDLI: Using Clifford Algebra to position a test fixture

Content Provider	IEEE Xplore Digital Library
Author	Waivio, N.
Copyright Year	2013
Description	Author affiliation: Defensive Syst. Div., Northrop Grumman Corp. Electron. Syst., Rolling Meadows, IL, USA (Waivio, N.)
Abstract	This paper is about using Clifford Algebra to position a gimbal test fixture that is used during infrared laser (IR) pointing system testing. The Clifford Algebra Cl3, 0 specifically known as the Algebra of Physical Space (APS) is useful as a unifying mathematical frame work in physics that can describe classical physics, special relativity, general relativity, electro-dynamics, and quantum mechanics in a consistent and concise way. This paper seeks to demonstrate the use of APS in controlling a simple 2 degree of freedom (DOF) gimbal system that would be useful for testing a 2DOF unit under test (UUT). The goal of the test is to rotate the UUT to a specific test position and point the UUT towards optical test equipment. This requires the accurate and reliable transformation of multiple reference frames and coordinate systems. The reason why APS is useful for rotations is because the even sub-algebra of APS is homomorphic to Hamilton's quaternion algebra. Clifford Algebra Cl3, 0 can be implemented numerically on a computer using the matrix representation of the Pauli algebra of 2×2 complex matrices. This paper will show the relationship between APS, quaternions, and Pauli matrices. The paper will also cover all of the basic operations of forming paravectors, rotors/eigenspinors, and converting to and from the matrix form. The paper will cover transformation and inverse transformations of reference frames and vectors in our example system.
Sponsorship	Aerosp. Electron. Syst. Soc.
Starting Page	1
Ending Page	5
File Size	1046474
Page Count	5
File Format	PDF
ISSN	10887725
e-ISBN	9781467356831
DOI	10.1109/AUTEST.2013.6645050
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-09-16
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Kinematics Matrix converters Lasers Quaternions Rotation Clifford Algebra Algebra of Physical Space Gimbal
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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