Simulation of system models containing zero-order causal paths. I.: Classification of zero-order causal paths. (English) Zbl 0757.65080
This paper relates the process of simulating a physical system from bond graph models in which there exist zero-order causal paths to systems of differential-algebraic equations (DAEs). Basically zero-order causal paths can arise algebraically in a loop if no integrating elements are present or if there exists a causal path between a storage element with derivative causality and a storage element with integral causality.
The concept of an essential causal cycle (which is a closed causal path which cannot be eliminated) is introduced which is used to classify 5 different classes of zero-order causal paths which are then related to different types of DAEs and their index of nilpotency.
Examples are given from electronic circuits and mechanical systems using bond graph models to illustrate these relationships.
The concept of an essential causal cycle (which is a closed causal path which cannot be eliminated) is introduced which is used to classify 5 different classes of zero-order causal paths which are then related to different types of DAEs and their index of nilpotency.
Examples are given from electronic circuits and mechanical systems using bond graph models to illustrate these relationships.
Reviewer: K.Burrage (Brisbane)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
| 34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
essential causal cycle; computer simulation; sequential causality assignment procedure; algebraic loops; bond graph models; zero-order causal paths; systems of differential-algebraic equations; index of nilpotency; electronic circuits; mechanical systemsCitations:
Zbl 0757.65081Software:
DASSLReferences:
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