scholarly journals Geometric properties of projective constraint violation stabilization method for generally constrained multibody systems on manifolds

2008 ◽  
Vol 20 (1) ◽  
pp. 107-107
Author(s):  
Zdravko Terze ◽  
Joris Naudet
Keyword(s):  
Multibody Systems ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Geometric Properties ◽  
Constrained Multibody Systems

Efficient Dynamic Analysis Method for Multibody Systems With Constraint Violation Stabilization Method

1999 ◽  
Author(s):  
Apiwat Reungwetwattana ◽  
Shigeki Toyama
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Analysis Method ◽  
Stabilization Method ◽  
Kinematic Constraint ◽  
Constraint Violation ◽  
Closed Loops ◽  
Constraint Stabilization ◽  
Constraint Equations ◽  
Crank Mechanism

Abstract This paper presents an efficient extension of Rosenthal’s order-n algorithm for multibody systems containing closed loops. Closed topological loops are handled by cut joint technique. Violation of the kinematic constraint equations of cut joints is corrected by Baumgarte’s constraint violation stabilization method. A reliable approach for selecting the parameters used in the constraint stabilization method is proposed. Dynamic analysis of a slider crank mechanism is carried out to demonstrate efficiency of the proposed method.

Orthogonal Complement-Based Divide and Conquer Algorithm: A Detailed Investigation of Its Performance

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Growth Rate ◽  
Arbitrary Number ◽  
Multibody Systems ◽  
Divide And Conquer ◽  
Orthogonal Complement ◽  
Error Growth ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Divide And Conquer Algorithm ◽  
Kinematic Loops

In this paper, we characterize the orthogonal complement-based divide-and-conquer (ODCA) [1] algorithm in terms of the constraint violation error growth rate and singularity handling capabilities. In addition, we present a new constraint stabilization method for the ODCA architecture. The proposed stabilization method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the performance of the ODCA with augmented [2] and reduction [3] methods. The results indicate that the performance of the ODCA falls between these two traditional techniques. Furthermore, using a numerical example, we demonstrate the effectiveness of the new stabilization scheme.

scholarly journals Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems

2003 ◽  
Author(s):  
Zdravko Terze ◽  
Joris Naudet ◽  
Dirk Lefeber
Keyword(s):  
Mathematical Models ◽  
Dynamic Simulation ◽  
Multibody Systems ◽  
Point Of View ◽  
Constraint Violation ◽  
Projective Method ◽  
Holonomic Constraints ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
Holonomic Systems

Constraint gradient projective method for stabilization of constraint violation during integration of constrained multibody systems is in the focus of the paper. Different mathematical models for constrained MBS dynamic simulation on manifolds are surveyed and violation of kinematical constraints is discussed. As an extension of the previous work focused on the integration procedures of the holonomic systems, the constraint gradient projective method for generally constrained mechanical systems is discussed. By adopting differentialgeometric point of view, the geometric and stabilization issues of the method are addressed. It is shown that the method can be applied for stabilization of holonomic and non-holonomic constraints in Pfaffian and general form.

A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Paulo Flores ◽  
Margarida Machado ◽  
Eurico Seabra ◽  
Miguel Tavares da Silva
Keyword(s):  
Parametric Study ◽  
Multibody Systems ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Forward Dynamics ◽  
Stabilization Method ◽  
Time Step ◽  
Constrained Multibody Systems ◽  
Laplace Transform Technique ◽  
Baumgarte Stabilization

This paper presents and discusses the results obtained from a parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. The main purpose of this work is to analyze the influence of the variables that affect the violation of constraints, chiefly the values of the Baumgarte parameters, the integration method, the time step, and the quality of the initial conditions for the positions. In the sequel of this process, the formulation of the rigid multibody systems is reviewed. The generalized Cartesian coordinates are selected as the variables to describe the bodies’ degrees of freedom. The formulation of the equations of motion uses the Newton–Euler approach, augmented with the constraint equations that lead to a set of differential algebraic equations. Furthermore, the main issues related to the stabilization of the violation of constraints based on the Baumgarte approach are revised. Special attention is also given to some techniques that help in the selection process of the values of the Baumgarte parameters, namely, those based on the Taylor’s series and the Laplace transform technique. Finally, a slider-crank mechanism with eccentricity is considered as an example of application in order to illustrate how the violation of constraints can be affected by different factors.

A Constraint Stabilization Method for Time Integration of Constrained Multibody Systems in Lie Group Setting

2014 ◽  
Author(s):  
Andreas Müller ◽  
Zdravko Terze
Keyword(s):  
Vector Space ◽  
Lie Group ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Iteration Step ◽  
Stabilization Method ◽  
Constrained Multibody Systems ◽  
Integration Schemes ◽  
Local Coordinates ◽  
Classical Vector

The stabilization of geometric constraints is vital for an accurate numerical solution of the differential-algebraic equations (DAE) governing the dynamics of constrained multibody systems (MBS). Although this has been a central topic in numerical MBS dynamics using classical vector space formulations, it has not yet been sufficiently addressed when using Lie group formulations. A straightforward approach is to impose constraints directly on the Lie group elements that represent the MBS motion, which requires additional constraints accounting for the invariants of the Lie group. On the other hand, most numerical Lie group integration schemes introduce local coordinates within the integration step, and it is natural to perform the stabilization in terms of these local coordinates. Such a formulation is presented in this paper for index 1 formulation. The stabilization method is applicable to general coordinate mappings (canonical coordinates, Cayley-Rodriguez, Study) on the MBS configuration space Lie group. The stabilization scheme resembles the well-known vectors space projection and pseudo-inverse method consisting in an iterative procedure. A numerical example is presented and it is shown that the Lie group stabilization scheme converges normally within one iteration step, like the scheme in the vector space formulation.

A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems

2009 ◽  
Author(s):  
Paulo Flores ◽  
Margarida Machado ◽  
Eurico Seabra ◽  
Miguel Tavares da Silva
Keyword(s):  
Parametric Study ◽  
Multibody Systems ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Forward Dynamics ◽  
Stabilization Method ◽  
Time Step ◽  
Constrained Multibody Systems ◽  
Laplace Transform Technique ◽  
Baumgarte Stabilization

This paper presents and discusses the results obtained from a parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. The main purpose of this work is to analyze the influence of the variables that affect the violation of constraints, chiefly the values of the Baumgarte parameters, the integration method, the time step and the quality of the initial conditions for the positions. In the sequel of this process the formulation of the rigid multibody systems is reviewed. The generalized Cartesian coordinates are selected as the variables to describe the bodies’ degrees of freedom. The formulation of the equations of motion uses the Newton-Euler approach that is augmented with the constraint equations that lead to a set of differential algebraic equations. Furthermore, the main issues related to the stabilization of the violation of constraints based on the Baumgarte approach are revised. Special attention is also given to some techniques that help in the selection process of the values of the Baumgarte parameters, namely those based on the Taylor’s series and Laplace transform technique. Finally, a slider crank mechanism with eccentricity is considered as an example of application in order to illustrated how the violation of constraints can be affected by different factors such as the Baumgarte parameters, integrator, time step and initial guesses.

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