Lie-group integration method for constrained multibody systems in state space

Terze, Zdravko and Müller, Andreas and Zlatar, Dario (2014) Lie-group integration method for constrained multibody systems in state space. = Lie-group integration method for constrained multibody systems in state space. Multibody System Dynamics. ISSN 1384-5640. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q2 (2013). Točan broj autora: 3. (In Press)

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Abstract

Coordinate-free Lie-group integration method of arbitrary (and possibly higher) order of accuracy for constrained multibody systems (MBS) is proposed in the paper. Mathematical model of MBS dynamics is shaped as a DAE system of equations of index 1, whereas dynamics is evolving on the system state space modeled as a Lie-group. Since the formulated integration algorithm operates directly on the system manifold via MBS elements’ angular velocities and rotational matrices, no local rotational coordinates are necessary, and kinematical differential equations (that are prone to singularities in the case of three-parameter-based local description of the rotational kinematics) are completely avoided. Basis of the integration procedure is the Munthe–Kaas algorithm for ODE integration on Lie-groups, which is reformulated and expanded to be applicable for the integration of constrained MBS in the DAE-index-1 form. In order to eliminate numerical constraint violation for generalized positions and velocities during the integration procedure, a constraint stabilization projection method based on constrained least-square minimization algorithm is introduced. Two numerical examples, heavy top dynamics and satellite with mounted 5-DOF manipulator, are presented. The proposed Lie-group DAE-index-1 integration scheme is easy-to-use for an MBS with kinematical constraints of general type, and it is especially suitable for dynamics of mechanical systems with large 3D rotations where standard (vector space) formulations might be inefficient due to kinematical singularities (three-parameter-based rotational coordinates) or additional kinematical constraints (redundant quaternion formulations). © 2014 Springer Science+Business Media Dordrecht

Item Type: Article (["eprint_fieldopt_article_type_article" not defined])
Keywords (Croatian): Algorithms; Differential equations; Dynamics; Least squares approximations; Lie groups; Mathematical models; Numerical methods; Stabilization; Vector spaces; Constraint violation; DAE systems; Integration algorithm; Multi-body systems dynamics; Numerical integration methods; Special orthogonal group; Integration
Subjects: NATURAL SCIENCES > Mathematics
TECHNICAL SCIENCE > Mechanical Engineering
TECHNICAL SCIENCE > Aviation, rocket and space technology
Divisions: 1300 Department of Aeronautical Engineering > 1320 Chair of Aircraft Dynamics
Indexed in Web of Science: No
Indexed in Current Contents: No
Quartiles: Q2 (2013)
Citations SCOPUS: 0 (3.6.2015.)
Date Deposited: 03 Jun 2015 07:37
Last Modified: 09 Apr 2020 18:55
URI: http://repozitorij.fsb.hr/id/eprint/4196

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