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Journal of Vibration and Control
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How to Improve Confidence in Calculations for Non-smooth Dynamical Systems

F. Schmidt

ENTPE, LGM, URA CNRS 1652 Rue Maurice Audin, F-69518 Vaulx-en-Velin, France ({schmidt, lamarque} @entpe.fr)

C.-H. Lamarque

ENTPE, LGM, URA CNRS 1652 Rue Maurice Audin, F-69518 Vaulx-en-Velin, France ({schmidt, lamarque} @entpe.fr)

In this paper we define an "indicator of tangent variation" that makes it possible to estimate the divergence between pathes starting from different initial conditions and/or parameters. First we work out theoretically this indicator; then we consider two examples: for the first one this indicator is well adapted. The second one corresponds to the case of an impact oscillator. In this case, grazing bifurcations can occur and prevent direct use of the defined indicator.

Key Words: Non-smooth dynamical systems • numerical calculations • uncertainty • grazing bifurcation

Journal of Vibration and Control, Vol. 14, No. 1-2, 231-253 (2008)
DOI: 10.1177/1077546307079406
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