Redundancy - Free Integration of Rotational Quaternions in Minimal Form

Terze, Zdravko and Mueller, Andreas and Zlatar, Dario (2014) Redundancy - Free Integration of Rotational Quaternions in Minimal Form. = Redundancy - Free Integration of Rotational Quaternions in Minimal Form. In: The ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2014), 17-20.08.2014., Buffalo, New York, USA.

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Abstract

Redundancy-free computational procedure for solving dynamics of rigid body by using quaternions as the rotational kinematic parameters will be presented in the paper. On the contrary to the standard algorithm that is based on redundant DAE-formulation of rotational dynamics of rigid body that includes algebraic equation of quaternions' unit-length that has to be solved during marching-in-time, the proposed method will be based on the integration of a local rotational vector in the minimal form at the Lie-algebra level of the SO(3) rotational group during every integration step. After local rotational vector for the current step is determined by using standard (possibly higher-order) integration ODE routine, the rotational integration point is projected to Sp(1) quaternion-group via pertinent exponential map. The result of the procedure is redundancy-free integration algorithm for rigid body rotational motion based on the rotational quaternions that allows for straightforward minimal-form-ODE integration of the rotational dynamics.

Item Type: Conference or Workshop Item (Lecture)
Keywords (Croatian): Time integration schemes, spatial rotations, rotational quaternions, Lie-groups, special orthogonal group SO(3), unit quaternion group, symplectic group Sp(1)
Subjects: TECHNICAL SCIENCE > Mechanical Engineering
TECHNICAL SCIENCE > Aviation, rocket and space technology
Divisions: 1300 Department of Aeronautical Engineering > 1320 Chair of Aircraft Dynamics
Date Deposited: 22 Sep 2016 13:44
Last Modified: 22 Sep 2016 13:44
URI: http://repozitorij.fsb.hr/id/eprint/6977

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