Using Rotations to Build Aerospace Coordinate Systems - Defence ...
Using Rotations to Build Aerospace Coordinate Systems - Defence ...
Using Rotations to Build Aerospace Coordinate Systems - Defence ...
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Page classification: UNCLASSIFIEDDEFENCE SCIENCE AND TECHNOLOGY ORGANISATIONDOCUMENT CONTROL DATA1. CAVEAT/PRIVACY MARKING2. TITLE<strong>Using</strong> <strong>Rotations</strong> <strong>to</strong> <strong>Build</strong> <strong>Aerospace</strong> <strong>Coordinate</strong><strong>Systems</strong>4. AUTHORDon Koks6a. DSTO NUMBERDSTO–TN–06408. FILE NUMBER2004/10929406b. AR NUMBERAR–013–4249. TASK NUMBERAIR 00/06913. URL OF ELECTRONIC VERSIONhttp://www.ds<strong>to</strong>.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 AUTHOR<strong>Systems</strong> Sciences Labora<strong>to</strong>ryP.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 DESCRIPTORSRotation<strong>Coordinate</strong>s19. ABSTRACTAxes of rotationSpace navigationPresented here are the main techniques necessary <strong>to</strong> understand rotations in three dimensions, for usewith global visualisation and aerospace simulations. Relevant techniques can be extremely difficult <strong>to</strong>find in textbooks, so some useful examples are collected here <strong>to</strong> 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 converting<strong>to</strong> and from the standard software pro<strong>to</strong>col 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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