Integration through singularities

Stossmeister T.

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Integration through singularities

机译：通过奇异性整合

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The numerical integration of the equations of motion of a multi-body system in index-1-formulation (differential-algebraic equations) sometimes breaks down, because there is a singularity on the manifold of consistent positions. This can be the case even if there is a continuously differentiable solution of the equations. In this article it is shown how to get through such singularities in very common situations by "blowing up" the position constraint equations. A very simple proof for the finiteness of the algorithm is given and explained with simple, but non-trivial examples. (C) 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. [References: 9]

机译：有时，由于一致位置的流形上存在奇异性，以指数1公式表示的多体系统运动方程（微分-代数方程）的数值积分有时会破坏。即使方程组存在连续可微解，情况也可能如此。本文显示了如何在非常常见的情况下通过“膨胀”位置约束方程式来克服这些奇点。给出了一个非常简单的算法有限性证明，并通过简单但不平凡的示例进行了解释。（C）2003 WILEY-VCH Verlag GmbH＆Co.KGaA，Weinheim。 [参考：9]

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2003年第10期|共15页
作者
Stossmeister T.;
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正文语种 eng
中图分类应用数学;
关键词
Multi-body system; Singularity; Blow-up;

机译：多体系统;奇点;爆炸;

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Integration through singularities

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