According to a recent paper (Laulusa and Bauchau, 2008, “Review of Classical Approaches for Constraint Enforcement in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 3(1), 011004), Maggi’s formulation is a simple and stable way to solve the dynamic equations of constrained multibody systems. Among the difficulties of Maggi’s formulation, Laulusa and Bauchau quoted the need for an appropriate choice (and change, when necessary) of independent coordinates, as well as the high cost of computing and updating the basis of the tangent null space of constraint equations. In this paper, index-1 Lagrange’s equations are first considered, including the not-so-rare case of having a singular mass matrix and redundant constraints. The existence and uniqueness of solution for acceleration vector and Lagrange multipliers vector is studied in a very simple way. Then, following Von Schwerin (Von Schwerin, Multibody System Simulation. Numerical Methods, Algorithms and Software, Springer, New York, 1999), Maggi’s formulation is described as the most efficient way (in general) to solve these index-1 equations. Next, an improved double-step method, which implements the matrix transformations of Maggi’s formulation in an efficient way, is described. Finally, two large real-life examples are presented.
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e-mail: javier.garciadejalon@upm.es
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April 2012
Research Papers
Efficient Solution of Maggi’s Equations
Javier García de Jalón,
Javier García de Jalón
ETSII and INSIA,
e-mail: javier.garciadejalon@upm.es
Technical University of Madrid (UPM)
, José Gutiérrez Abascal 2, 28006 Madrid, Spain
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Andrés F. Hidalgo
e-mail: andres.francisco.hidalgo@upm.es
Andrés F. Hidalgo
INSIA, Technical University of Madrid (UPM)
, Campus Sur UPM, Ctra. Valencia km 7, 28031 Madrid, Spain
Search for other works by this author on:
Javier García de Jalón
ETSII and INSIA,
Technical University of Madrid (UPM)
, José Gutiérrez Abascal 2, 28006 Madrid, Spain
e-mail: javier.garciadejalon@upm.es
Andrés F. Hidalgo
INSIA, Technical University of Madrid (UPM)
, Campus Sur UPM, Ctra. Valencia km 7, 28031 Madrid, Spain
e-mail: andres.francisco.hidalgo@upm.es
J. Comput. Nonlinear Dynam. Apr 2012, 7(2): 021003 (10 pages)
Published Online: December 22, 2011
Article history
Received:
May 16, 2011
Revised:
October 3, 2011
Online:
December 22, 2011
Published:
December 22, 2011
Citation
García de Jalón, J., Callejo, A., and Hidalgo, A. F. (December 22, 2011). "Efficient Solution of Maggi’s Equations." ASME. J. Comput. Nonlinear Dynam. April 2012; 7(2): 021003. https://doi.org/10.1115/1.4005238
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