On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 1

1977 ◽  
Vol 99 (3) ◽  
pp. 773-779 ◽  
Author(s):  
N. Orlandea ◽  
M. A. Chace ◽  
D. A. Calahan
Keyword(s):  
Computer Simulation ◽  
Dynamic Analysis ◽  
Numerical Solutions ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Front Suspension ◽  
Analysis And Design

The work described herein is an extension of sparse matrix and stiff integrated numerical algorithms used for the simulation of electrical circuits and three-dimensional mechanical dynamic systems. By applying these algorithms big sets of sparse linear equations can be solved efficiently, and the numerical instability associated with widely split eigenvalues can be avoided. The new numerical methods affect even the initial formulation for these problems. In this paper, the equations of motion and constraints (Part 1) and the force function of springs and dampers (Part 2) are set up, and the numerical solutions for static, transient, and linearized types of analysis as well as the modal optimization algorithms are implemented in the ADAMS (automatic dynamic analysis of mechanical systems) computer program for simulation of three-dimensional mechanical systems (Part 2). The paper concludes with two examples: computer simulation of the front suspension of a 1973 Chevrolet Malibu and computer simulation of the landing gear of a Boeing 747 airplane. The efficiency of simulation and comparison with experimental results are given in tabular form.

An Adaptive Constraint Violation Stabilization Method for Dynamic Analysis of Mechanical Systems

1985 ◽  
Vol 107 (4) ◽  
pp. 488-492 ◽  
Author(s):  
C. O. Chang ◽  
P. E. Nikravesh
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
General Purpose ◽  
Adaptive Mechanism ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Transient Dynamic Analysis ◽  
Constrained Mechanical Systems ◽  
Feedback Control Theory

The transient dynamic analysis of equations of motion for constrained mechanical systems requires the solution of a mixed set of algebraic and differential equations. A constraint violation stabilization method, based on feedback control theory of linear systems, has been suggested by some researchers for solving these equations. However, since the value of damping parameters for this method are uncertain, the method is to some extent unattractive for general-purpose use. This paper presents an adaptive mechanism for determining the damping parameters. The results of the simulation for two examples illustrate the improvement in reducing the constraint violations when using this method.

A Gauge-Invariant Formulation for Constrained Mechanical Systems Using Square-Root Factorization and Unitary Transformation

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Farhad Aghili
Keyword(s):  
Motion Control ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Control Action ◽  
Gauge Invariant ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
Weighting Matrix ◽  
Rotational Components ◽  
Invariant Formulation

A gauge-invariant formulation for deriving the dynamic equations of constrained multibody systems in terms of (reduced) quasivelocities is presented. This formulation does not require any weighting matrix to deal with the gauge-invariance problem when both translational and rotational components are involved in the generalized coordinates or in the constraint equations. Moreover, in this formulation the equations of motion are decoupled from those of constrained force, and each system has its own independent input. This allows the possibility to develop a simple force control action that is totally independent from the motion control action facilitating a hybrid force/motion control. Tracking force/motion control of constrained multibody systems based on a combination of feedbacks on the vectors of the quasivelocities and the configuration-variables are presented.

A Comparative Study on Some Different Formulations of the Dynamic Equations of Constrained Mechanical Systems

1987 ◽  
Vol 109 (4) ◽  
pp. 466-474 ◽  
Author(s):  
J. Unda ◽  
J. Garci´a de Jalo´n ◽  
F. Losantos ◽  
R. Enparantza
Keyword(s):  
Comparative Study ◽  
Relative Efficiency ◽  
Multibody Systems ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Dynamic Equations ◽  
Natural Coordinates ◽  
Constrained Mechanical Systems ◽  
Computer Codes

This paper presents a comparative theoretical and numerical study on the efficiency of several numerical methods for the dynamic analysis of constrained mechanical systems, also called in the literature multibody systems. This comparative study has been performed between methods based on the use of “reference point” coordinates and those based on the use of “natural” coordinates. This study embraces different possibilities to formulate the differential equations of motion. The relative efficiency of the resulting algorithms has been analyzed theoretically in terms of the number of multiplications needed to evaluate the mechanism accelerations. This efficiency has also been studied implementing the methods into computer codes and testing them with different examples. Conclusions on the relative efficiency of the methods are finally presented.

A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 2

1977 ◽  
Vol 99 (3) ◽  
pp. 780-784 ◽  
Author(s):  
N. Orlandea ◽  
D. A. Calahan ◽  
M. A. Chace
Keyword(s):  
Computer Simulation ◽  
Dynamic Analysis ◽  
Numerical Solutions ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Front Suspension ◽  
Analysis And Design

The work described herein is an extension of sparse matrix and stiff integrated numerical algorithms used for the simulation of electrical circuits and three-dimensional mechanical dynamic systems. By applying these algorithms, big sets of sparse linear equations can be solved efficiently, and the numerical instability associated with widely split eigenvalues can be avoided. The new numerical methods affect even the initial formulation for these problems. In this paper, the equations of motion and constraints (Part 1) and the force function of springs and dampers (Part 2) are set up, and the numerical solutions for static, transient, and linearized types of analysis as well as the model optimization algorithms are implemented in the ADAMS (automatic dynamic analysis of mechanical systems) computer program for simulation of three-dimensional mechanical systems (Part 2). The paper concludes with two examples: computer simulation of the front suspension of a 1973 Chevrolet Malibu and computer simulation of the landing gear of a Boeing 747 airplane. The efficiency of simulation and comparison with experimental results are given in tabular form.

scholarly journals Principle of compatibility and non-generalised coordinates

2005 ◽  
Vol 27 (2) ◽  
pp. 74-85
Author(s):  
Dinh Van Phong
Keyword(s):  
Lagrange Multipliers ◽  
Theoretical Basis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Special Treatment ◽  
System Of Equations ◽  
Constrained Mechanical Systems ◽  
Generalised Coordinates

The contribution is devoted to using so-called non-generalised coordinates for deriving the system of equations of motion. Differently from common techniques for constrained mechanical systems the principle of compatibility is chosen as the tool. This takes the advantage in the possibility for extension to systems with nonideal constraints, however, the special treatment is needed. In the article the author derived the theoretical basis as well as numerical algorithms concerning the combination of nongeneralised coordinates with the principle of compatibility. Some comparisons of the technique under consideration and usual technique using Lagrange multipliers are discussed. Some examples are shown for illustration. The case of contact of moving disc on the surface is given in detail

Application of the Canonical Equations of Motion in Problems of Constrained Multibody Systems With Intermittent Motion

1988 ◽  
Author(s):  
H. M. Lankarani ◽  
P. E. Nikravesh
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Momentum Balance ◽  
Constrained Multibody Systems ◽  
Intermittent Motion

Abstract For mechanical systems that undergo intermittent motion, the usual formulation of the equations of motion is not valid over the periods of the discontinuity, and a procedure for balancing the momenta of the system is often performed. A canonical form of the equations of motion is used here as the differential equations of motion. A set of momentum balance-impulse equations are derived in terms of the system total momenta by explicitly integrating the canonical equations. The method shows to be stable while numerically integrating the canonical equations, and efficient while solving the momentum balance-impulse equations. Examples are provided to illustrate the validity of the method.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

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