Convergence Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints

1993 ◽  
Vol 30 (5) ◽  
pp. 1467-1482 ◽  
Author(s):  
Edda Eich
Keyword(s):  
Projection Method ◽  
Mechanical Systems ◽  
Coordinate Projection ◽  
Convergence Results ◽  
Algebraic Constraints

Projection Method With Minimal Correction Procedure for Numerical Simulation of Constrained Dynamics

2017 ◽  
Author(s):  
Patrick S. Heaney ◽  
Gene Hou
Keyword(s):  
Projection Method ◽  
Numerical Technique ◽  
Correction Method ◽  
Differential Algebraic Equations ◽  
Constrained Systems ◽  
Correction Procedure ◽  
Algebraic Equations ◽  
Differential Algebraic Equation ◽  
Index Reduction ◽  
Algebraic Constraints

This paper describes a numerical technique for simulating the dynamics of constrained systems, which are described generally by differential-algebraic equations. The Projection Method for index reduction of a differential-algebraic equation and a minimal correction procedure are described. This procedure ensures algebraic constraints are satisfied during the numerical integration of the reduced index system of differential equations. Two examples illustrate how the method can be utilized to solve constrained multibody and rotational dynamics problems. The efficiency and accuracy of the proposed index-reduction and minimal correction method are then evaluated.

UNIFORM CONVERGENCE OF MONOTONE MEASURE DIFFERENTIAL INCLUSIONS: WITH APPLICATION TO THE CONTROL OF MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

2008 ◽  
Vol 18 (05) ◽  
pp. 1435-1457 ◽  
Author(s):  
REMCO I. LEINE ◽  
NATHAN VAN DE WOUW
Keyword(s):  
Uniform Convergence ◽  
Differential Inclusions ◽  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Unilateral Constraints ◽  
Monotonicity Properties ◽  
Maximal Monotonicity ◽  
Convergence Results ◽  
Measure Differential Inclusions ◽  
Monotone Measure

In this paper, we present theorems which give sufficient conditions for the uniform convergence of measure differential inclusions with certain maximal monotonicity properties. The framework of measure differential inclusions allows us to describe systems with state discontinuities. Moreover, we illustrate how these convergence results for measure differential inclusions can be exploited to solve tracking problems for certain classes of nonsmooth mechanical systems with friction and one-way clutches. Illustrative examples of convergent mechanical systems are discussed in detail.

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