Lagrangian/Eulerian Description of Dynamic System
Publication: Journal of Engineering Mechanics
Volume 124, Issue 8
Abstract
This paper briefly reviews the two complementary descriptions of a dynamical system in its phase space as follows: (1) The Lagrangian point-of-view (leading to either a Monte Carlo simulation or a Gibbs set evolution study); and (2) the Eulerian point-of-view (leading to the global analytical equations governing the dynamics of mechanical systems, like the Liouville and the Fokker-Planck equations (FPE), and to the cell method in a numerical context). It points out the characteristics that a numerical method must show to obtain a correct description of the system dynamics and moves with the continuity from deterministic problems to chaotic and/or stochastic situations. The aim of this paper is the implementation of numerical techniques making the study of realistic problems possible. For this purpose, a preliminary academic example deals with the Duffing oscillator to assess the effectiveness of the developed numerical scheme. The second example pursues the assessment of the failure probability of a tank structure under nonstationary excitation.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 124 • Issue 8 • August 1998
Pages: 901 - 911
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Aug 1, 1998
Published in print: Aug 1998
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