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Research Papers

A Modular Modeling Approach to Simulate Interactively Multibody Systems With a Baumgarte/Uzawa Formulation

[+] Author and Article Information
Pierre Joli

Laboratoire IBISC, Université d’Evry-Val d’Essonne, 40 rue du Pelvoux, 91020 Evry, Francepjoli@iup.univ-evry.fr

Nicolas Séguy

Laboratoire IBISC, Université d’Evry-Val d’Essonne, 40 rue du Pelvoux, 91020 Evry, France

Zhi-Qiang Feng

Laboratoire de Mécanique d’Evry, Université d’Evry-Val d’Essonne, 40 rue du Pelvoux, 91020 Evry, France

J. Comput. Nonlinear Dynam 3(1), 011011 (Dec 10, 2007) (8 pages) doi:10.1115/1.2815331 History: Received October 03, 2006; Revised June 29, 2007; Published December 10, 2007

In this paper, a modular modeling approach of multibody systems adapted to interactive simulation is presented. This work is based on the study of the stability of two differential algebraic equation solvers. The first one is based on the acceleration-based augmented Lagrangian formulation and the second one on the Baumgarte formulation. We show that these two solvers give the same results and have to satisfy the same criteria to stabilize the algebraic constraint acceleration error. For a modular modeling approach, we propose to use the Baumgarte formulation and an iterative Uzawa algorithm to solve external constraint forces. This work is also the first step to validate the concept of two types of numerical components for object-oriented programming.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometric interpretation of a constrained system

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Figure 2

Position error of particle P

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Figure 3

Basic principle of the modular modeling

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Figure 4

Double pendulum modeled with relative joint coordinates

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Figure 5

Double pendulum modeled with fully Cartesian coordinates

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Figure 6

Trajectory of the mass m2 (centralized modeling)

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Figure 7

Comparison between centralized and modular modeling

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Figure 8

Comparison between centralized and modular modeling

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Figure 9

Interactive simulation of the double pendulum with FER/MECH

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Figure 10

Trajectory of the mass m2: Δt=10−2s

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