Using Rotations to Build Aerospace Coordinate Systems - Defence ...

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Head of Aerospace and Mechanical Engineering, ADFA 1Serials Section (M List), Deakin University Library, Geelong, Doc. Data SheetVictoriaHargrave Library, Monash UniversityDoc. Data SheetLibrarian, Flinders University 1OUTSIDE AUSTRALIAINTERNATIONAL DEFENCE INFORMATION CENTRESUS: Defense Technical Information CenterUK: DSTL Knowledge ServicesCanada: Defence Research Directorate R&D Knowledge andInformation Management (DRDKIM)1 (pdf format)1 (pdf format)NZ: Defence Information Centre 1ABSTRACTING AND INFORMATION ORGANISATIONSLibrary, Chemical Abstracts Reference Service 1Engineering Societies Library, US 1Materials Information, Cambridge Scientific Abstracts, US 1Documents Librarian, The Center for Research Libraries, US 1INFORMATION EXCHANGE AGREEMENT PARTNERSNational Aerospace Laboratory, Japan 1National Aerospace Laboratory, Netherlands 1SPARESDSTO Edinburgh Library 51Total number of printed copies: 43
Page classification: UNCLASSIFIEDDEFENCE SCIENCE AND TECHNOLOGY ORGANISATIONDOCUMENT CONTROL DATA1. CAVEAT/PRIVACY MARKING2. TITLEUsing Rotations to Build Aerospace CoordinateSystems4. AUTHORDon Koks6a. DSTO NUMBERDSTO–TN–06408. FILE NUMBER2004/10929406b. AR NUMBERAR–013–4249. TASK NUMBERAIR 00/06913. URL OF ELECTRONIC VERSIONhttp://www.dsto.defence.gov.au/corporate/reports/DSTO–TN–0640.pdf10. SPONSORDGAD15. SECONDARY RELEASE STATEMENT OF THIS DOCUMENTApproved For Public Release3. SECURITY CLASSIFICATIONDocumentTitleAbstract(U)(U)(U)5. CORPORATE AUTHORSystems Sciences LaboratoryP.O. Box 1500Edinburgh, SA 5111Australia6c. TYPE OF REPORTTechnical Note11. NO. OF PAGES3114. RELEASE AUTHORITY7. DOCUMENT DATEMarch, 200612. NO. OF REFS2Chief, Electronic Warfare and Radar DivisionOVERSEAS ENQUIRIES OUTSIDE STATED LIMITATIONS SHOULD BE REFERRED THROUGH DOCUMENT EXCHANGE, P.O. BOX 1500,EDINBURGH, SA 5111, AUSTRALIA16. DELIBERATE ANNOUNCEMENTNo Limitations17. CITATION IN OTHER DOCUMENTSNo Limitations18. DEFTEST DESCRIPTORSRotationCoordinates19. ABSTRACTAxes of rotationSpace navigationPresented here are the main techniques necessary to understand rotations in three dimensions, for usewith global visualisation and aerospace simulations. Relevant techniques can be extremely difficult tofind in textbooks, so some useful examples are collected here to highlight these techniques.The three standard aerospace coordinate systems are described and built using rotations. The mathematicsof rotations is described, using both matrices and quaternions. The necessary calculations aregiven for analysing standard scenarios that involve the Global Positioning Satellite system for findingline-of-sight directions on Earth, as well as for visualising the world from a cockpit, and for convertingto and from the standard software protocol for distributed interactive simulation environments.Appendices then discuss combining rotations, conversions with a particular type of Euler angle convention,the dangers of confusing Euler angles with incremental rotations for software writers, and finallythere is a short dicussion of interpolation of rotations in computing.Page classification: UNCLASSIFIED
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Page 12 and 13: DSTO-TN-0640ZmeridianPrimeYXEquator
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Page 18 and 19: DSTO-TN-0640nθx ′xFigure 4: The
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Page 22 and 23: DSTO-TN-0640ZNDEN 0E 0D 0 N 1E 1ω
Page 24 and 25: DSTO-TN-0640The vector giving the p
Page 26 and 27: DSTO-TN-0640Equation (2.2) together
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