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Integration through singularities
Author(s) -
Stoßmeister T.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310071
Subject(s) - gravitational singularity , singularity , simple (philosophy) , mathematics , constraint (computer aided design) , manifold (fluid mechanics) , differentiable function , mathematical analysis , position (finance) , numerical integration , algebraic equation , differential equation , equations of motion , classical mechanics , physics , geometry , nonlinear system , mechanical engineering , philosophy , epistemology , finance , quantum mechanics , engineering , economics
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.