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1

Implementation of A Geometric Constraint Regularization For Multibody System Models

Müller A.

Archive of Mechanical Engineering

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2014

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Vol. LXI, nr 2

365--383

EN

Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.

PL

Nadmiarowe więzy w układach wieloczłonowych (MBS) poważnie pogarszają wydajność obliczeniową i dokładność numerycznych metod symulacji systemów MBS. Klasycznym podejściem do rozwiązania tego problemu jest numeryczna dekompozycja Jakobianu więzów w kolejnych krokach całkowania cyfrowego. Dekompozycje takie są jednak kosztowne obliczeniowo. W artykule zaprezentowano metodę eliminacji, która wymaga tylko pojedynczej dekompozycji na etapie wstępnego przetwarzania modelu, a nie w trakcie integracji czasowej. Metoda jest oparta na wyznaczaniu przestrzeni ruchu przy wykorzystaniu koncepcji grup Liego. Pozwala ona zredukować zbiór więzów pętli dla szerokiej klasy systemów technicznych, przy czym w każdym przypadku zachowuje ona dostateczną liczbę więzów. Metoda została wyprowadzona i zilustrowana dla pojedynczych pętli kinematycznych.

2

Invariance of integro-differential equations with moving region of integration

Zawistowski Z. J.

Journal of Technical Physics

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2006

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Vol. 47, no 2

103-112

EN

General criterion of invariance of integro-differential equations under the Lie symmetry group of point transformations is derived. It is a generalization of the previous form of the criterion to the case of a moving range of integration. This is the situation when a region of integration depends on external, with respect to integration, variables what leads to its explicit dependence on a group parameter, so the region of integration moves under symmetry transformations. General case of dependence on independent and dependent variables and their derivatives is considered.

3

Application of the lie group theory to the analysis of flows in a turbulent boundary layer utilizing different turbulent viscosity models

Avramenko A. A., Kobzar S. G., Kuznetsov A. V., Bowen P. J.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

543-557

EN

The properties of symmetry of turbulent boundary layer flows are studied utilizing the Lie group theory. The self-similar forms of the independent variables and the solution functions for the boundary-layer type flows for four models of turbulent viscosity are obtained. The developed approach of finding a self-similar transformation for turbulent boundary-layer problems makes it possible to obtain numerical and simplified analytical solutions for a number of important flow situations.

4

A Stabilizing Control Law for Invariant Systems on Lie Groups

Apostolou N., Kazakos D.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 2

273-282

EN

This paper deals with the stabilizability of invariant control systems defined on Lie groups. A stabilization technique is presented which, under certain hypotheses, can lead to a criterion assuring the existence of a feedback controller which steers every initial condition to a specified target point of the state space of these systems.

5

Multivariable regular variation of functions and measures

Meerschaert M. M., Scheffler H.-P.

Journal of Applied Analysis

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1999

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Vol. 5, nr 1

125-146

EN

Regular variation is an asymptotic property of functions and measures. The one variable theory is well-established, and has found numerous applications in both pure and applied mathematics. In this paper we present several new results on mul-tivariable regular variation for functions and measures.

6

On symmetries of integro-differential equations

Zawistowski Z.J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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1998

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Vol. 46, nr 2

187-197

EN

A new, general method is presented for the determination of Lie symmetry groups of integro-differential equations. The exhibited method is a natural extension of the famous Ovsiannikov method developed for differential equations. The method leads to significant applications for instance to the Vlasov-Maxwell equations, which are integro-differential type irreducible to differential equations.