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master's thesis
Numerička integracija rotacijskih kvaterniona
Zagreb: University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 2015. urn:nbn:hr:235:698090
Pandža, Viktor
University of Zagreb
Faculty of Mechanical Engineering and Naval Architecture

Institutional repository: Repository of Faculty of Mechanical Engineering and Naval Architecture University of Zagreb

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Pandža, V. (2015). Numerička integracija rotacijskih kvaterniona (Master's thesis). Zagreb: University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture. Retrieved from https://urn.nsk.hr/urn:nbn:hr:235:698090

Pandža, Viktor. "Numerička integracija rotacijskih kvaterniona." Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 2015. https://urn.nsk.hr/urn:nbn:hr:235:698090

Pandža, Viktor. "Numerička integracija rotacijskih kvaterniona." Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 2015. https://urn.nsk.hr/urn:nbn:hr:235:698090

Pandža, V. (2015). 'Numerička integracija rotacijskih kvaterniona', Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, accessed 27 December 2024, https://urn.nsk.hr/urn:nbn:hr:235:698090

Pandža V. Numerička integracija rotacijskih kvaterniona [Master's thesis]. Zagreb: University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture; 2015 [cited 2024 December 27] Available at: https://urn.nsk.hr/urn:nbn:hr:235:698090

V. Pandža, "Numerička integracija rotacijskih kvaterniona", Master's thesis, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:235:698090

Metadata
TitleNumerička integracija rotacijskih kvaterniona
Title (english)Numerical integration of rotational quaternions
AuthorViktor Pandža
MentorZdravko Terze (mentor)
GranterUniversity of Zagreb
Faculty of Mechanical Engineering and Naval Architecture
Zagreb
Defense date and country2015-12-04, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Mechanical Engineering
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Aviation, Rocket and Space Technology
Abstract
U ovom radu opisana je numerička integracija kvaterniona u svrhu opisivanja rotacije krutog tijela u prostoru. Nakon izvoda potrebnih matematičkih modela, prikazani su algoritmi standardnih metoda integracije koji operiraju u vektorskim prostorima te algoritam nove metode koja operira izravno na rotacijskoj grupi SO(3) krutog tijela. Dok je u standardnim metodama svojstvo jedinične norme rotacijskog kvaterniona zadovoljeno dodavanjem dodatne stabilizacijske jednadžbe, čime se dobiva diferencijalno-algebarski sustav jednadžbi, nova metoda, već svojom konstrukcijom, zadovoljava to svojstvo čime se u konačnici dobiva sustav običnih diferencijalnih jednadžbi. U svrhu usporedbe opisanih metoda integracije rotacijskih kvaterniona provedeni su numerički eksperimenti na primjerima nestabilne rotacije slobodnog krutog tijela, na rotaciji krutog tijela s jednom uporišnom točkom te na praktičnom primjeru rotacije svemirskog objekta pomoću tri reakcijska diska.
Abstract (english)
Numerical integration of unit quaternions used for describing rigid body rotation is addressed in this thesis. After deriving necessary mathematical models, standard integration algorithms, which operate in vector space, are presented together with novel integration scheme, which operates on rotational group SO(3) of rigid body. While standard methods include additional equation for satisfying quaternion unit-length condition leading to a system of differential-algebraic equations (DAE), novel method inherently respects the unit-length condition leading to a system of ordinary differential equations (ODE). Described integration methods are compared on results of numerical experiments conducted on examples of unstable rigid body rotation, heavy top and on practical example of spacecraft rotation induced by using three reaction wheels.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:235:698090
Study programmeTitle: Mechanical Engineering
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra inženjer/inženjerka strojarstva (magistar/magistra inženjer/inženjerka strojarstva)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-05-28 10:19:04