Kinematička rekonstrukcija rotacije satelita

master's thesis

• Title (english): Kinematic reconstruction of satelite rotational motion
• Author: Michael Ban
• Mentor: Zdravko Terze (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2018-01-25, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

U ovom radu opisana je kinematička rekonstrukcija rotacije satelita, koja je provedena na realnom RAX-1 nanosatelitu. Na početku rada opisano je gibanje krutog tijela, koje se može prikazati u matričnom obliku pomoću SE(3) grupe. Zatim je predstavljena SO(3) grupa, koja predstavlja rotaciju krutog tijela. Budući da parametrizacija pomoću SO(3) grupe zahtijeva upotrebu devet parametara, od kojih su samo tri nezavisna, prikazana je parametrizacija rotacije pomoću Eulerovih kuteva. Pojava singulariteta prilikom opisivanja rotacija u 3D prostoru pomoću tri parametra (poput Eulerovih kuteva), vodi do potrebe za uvođenjem kvaterniona, kod kojih to nije slučaj. Ograničavanjem kvaterniona na jediničnu duljinu, dolazi se do jediničnog kvaterniona, koji se može sastojati od Eulerovih parametara. U nastavku su prikazane dvije standardne formulacije za numeričku integraciju na kvaternionima, te nova metoda, kojom se implicitno zadovoljava jedinična norma kvaterniona, te ju nije potrebno uvoditi kao dodatnu algebarsku jednadžbu, čime bi se trebao ubrzati proces numeričke integracije. Na kraju je prikazan primjer kinematičke rekonstrukcije realnog RAX-1 satelita, kod koje se uspoređuju dvije metode integracije - nova metoda i metoda kod koje se eksplicitno zadovoljava jedinična norma kvaterniona.

Abstract (english)

In this thesis, kinematic reconstruction of satelite rotational motion is described, which is implemented to real RAX-1 nanosatellite. In the begining, rigid body motion is written in matrix form and described in terms of SE(3) group. After that, SO(3) group is described, which represents rotational motion of rigid body. Since parameterization using SO(3) group uses nine parameters, only three of which are independent, parametrization in terms of Euler angles is showed. The fact that singularities appear when three-parameter parametrization is used to describe 3D rotational motion (e.g. Euler angles), there is a need to introduce quaternions, which are singularity-free. Constraining the quaternion to unit norm, we get unit quaternion, which can also include Euler parameters. Furthermore, two standard methods for numerical integration on quaternions are introduced, along with new method, in which unit norm of quaternion is implicitly satisfied and therefore there is no need to introduce additional algebraic equation, which should lead to increased efficiency in numerical integration. At the end, kinematic reconstruction of real RAX-1 nanosatellite is made, during which two integration methods are compared - new method and method in which unit norm of quaternion is explicitly satisified.

• Keywords: kruto tijelo; rotacija u 3D prostoru; SO(3) grupa; jedinični kvaternioni; numerička integracija
• Keywords (english): rigid body; 3D rotational motion; SO(3) group; unit quaternion; numerical integration
• Language: croatian
• URN:NBN: urn:nbn:hr:235:415775
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka strojarstva (magistar/magistra inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-05-22 21:11:53