An automatic constraint violation stabilization method for differential/ algebraic equations of motion in multibody system dynamics

2000 ◽  
Vol 21 (1) ◽  
pp. 103-108 ◽  
Author(s):  
Zhao Weijia ◽  
Pan Zhenkuan ◽  
Wang Yibing
Keyword(s):  
System Dynamics ◽  
Multibody System ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Multibody System Dynamics ◽  
Algebraic Equations ◽  
Stabilization Method ◽  
Constraint Violation

scholarly journals L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Bowen Li ◽  
Jieyu Ding ◽  
Yanan Li
Keyword(s):  
System Dynamics ◽  
Multibody System ◽  
Differential Algebraic Equations ◽  
Multibody System Dynamics ◽  
Dynamics Simulation ◽  
Time Interval ◽  
Algebraic Equations ◽  
Stable Method ◽  
Long Term Conditions ◽  
Equidistant Nodes

An L-stable method over time intervals for differential-algebraic equations (DAEs) of multibody system dynamics is presented in this paper. The solution format is established based on equidistant nodes and nonequidistant nodes such as Chebyshev nodes and Legendre nodes. Based on Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula are obtained by comparison with Pade approximation. Newton iteration method is used during the solution process. Taking the planar two-link manipulator system as an example, the results of L-stable method presented are compared for different number of nodes in the time interval and the step size in the simulation, and also compared with the classic Runge-Kutta method, A-stable method, Radau IA, Radau IIA, and Lobatto IIIC methods. The results show that the method has the advantages of good stability and high precision and is suitable for multibody system dynamics simulation under long-term conditions.

Two Friction’s Laws for Lagrange’s Equations of Multibody System with Dry Friction

2011 ◽  
Vol 328-330 ◽  
pp. 1697-1700
Author(s):  
Jian Feng Wang ◽  
Ying Jiu Liu ◽  
Shun Chuan Gao ◽  
Song Li ◽  
Feng Feng
Keyword(s):  
System Dynamics ◽  
Dry Friction ◽  
Multibody System ◽  
Differential Algebraic Equations ◽  
Multibody System Dynamics ◽  
Algebraic Equations ◽  
Friction Forces ◽  
Friction Law ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

With the first kind of Lagrange’s equations, this paper presents the dynamical equations of multibody system with friction constraints. The generalized forces of friction forces are described in the form of matrix. Considering numerical method is widespread to analyze the characteristics of multibody system dynamics, this paper compares the two friction laws for solving the multibody system problem with dry friction constraints. Using Baumgarte’s and augmentation method, the differential-algebraic equations are given in the form of differential equations matrix to raise calculating efficiency. The friction force for Coulomb’s friction law and the continuous friction law is denoted, which converts subsection smooth systems to continuous smooth systems. An example is given to evaluate the validity of continuous law of friction. The numerical simulation shows that continuous law of friction is an effective method to process multibody system friction problem. The work in this paper also provides a new direction to research the non-smooth multibody system dynamics equation.

The Automatic Stabilization Algorithm for Euler-Lagrange Equations With Holonomic/Nonholonomic Constraints in Multibody System Dynamics

2001 ◽  
Author(s):  
Zhenkuan Pan ◽  
Weijia Zhao
Keyword(s):  
System Dynamics ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Multibody System Dynamics ◽  
Integration Step ◽  
Lagrange Equations ◽  
Constraint Violation ◽  
Automatic Stabilization ◽  
The One

Abstract A new automatic constraint violation stabilization algorithm for numerical integration of Euler-Lagrange equations of motion of multibody system dynamics based on Baumgarte constraint violation stabilization method and Taylor expansion of constraint functions is presented. The constraint equations may be holonomic or nonholonomic. The parameters α, β, σ used in Baumgarte’s method are determined automatically according to integration step. Some numerical examples compare the accuracy between the traditional method and the one suggested in this paper are presented finally.

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