On the choice of configuration space for numerical Lie group integration of constrained rigid body systems

Müller, Andreas and Terze, Zdravko (2014) On the choice of configuration space for numerical Lie group integration of constrained rigid body systems. = On the choice of configuration space for numerical Lie group integration of constrained rigid body systems. Journal of Computational and Applied Mathematics, 262. pp. 3-13. ISSN 0377-0427. Vrsta rada: ["eprint_fieldopt_article_type_article" not defined]. Kvartili JCR: Q2 (2013). Točan broj autora: 2.

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Abstract

Standard numerical integration schemes for multibody system (MBS) models in absolute coordinates neglect the coupling of linear and angular motions since finite positions and rotations are updated independently. As a consequence geometric constraints are violated, and the accuracy of the constraint satisfaction depends on the integrator step size. It is discussed in this paper that in certain cases perfect constraint satisfaction is possible when using an appropriate configuration space (without numerical constraint stabilization). Two formulations are considered, one where R3 is used as rigid body configuration space and another one where rigid body motions are properly modeled by the semidirect product SE(3)=SO(3)â‰R3. MBS motions evolve on a Lie group and their dynamics is naturally described by differential equations on that Lie group. In this paper the implications of using the two representations on the constraint satisfaction within Munthe-Kaas integration schemes are investigated. It is concluded that the SE(3) update yields perfect constraint satisfaction for bodies constrained to a motion subgroup of SE(3), and in the general case both formulations lead to equivalent constraint satisfaction.

Item Type: Article (["eprint_fieldopt_article_type_article" not defined])
Keywords (Croatian): Constraint Satisfaction; Multi Body Systems; Munthe-Kaas scheme; Rigidbody dynamics; Screw systems; Differential equations; Lie groups; Rigid structures; Wave functions; 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: Yes
Indexed in Current Contents: Yes
Quartiles: Q2 (2013)
Date Deposited: 20 May 2015 09:32
Last Modified: 18 Feb 2016 16:28
URI: http://repozitorij.fsb.hr/id/eprint/4315

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