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Models and Algorithms for Non-Smooth Lagrangian Systems under Normal Cone Inclusion

Dry friction and impacts lead to discontinuities in the acceleration and the velocity of a mechanical system. Within the framework of Lagrangian mechanics, an algorithm is presented which is able to treat such discontinuity events and to determine the associated state transitions in a most consistent and reliable way. By starting off with Lagrange's equations of second kind, additional contact forces are taken into account by Lagrangian multipliers and are equipped with maximal monotone set-valued constitutive laws, which turn the second order differential equations of the dynamical system into differential inclusions in the sense of Filippov. Generalized Newtonian impact laws in inequality form are consistently embedded into this framework by taking the system's acceleration as the differential measures of its velocity. The resulting measure differential inclusions are discretized on velocity level by an implicit time-stepping scheme. The set-valued constitutive laws are assumed to be of normal cone type, which relates the problem to optimization theory. For solving the normal cone inclusions, equivalent proximal point problems are formulated and numerically treated by a Gauss-Seidel iteration. This complies with the augmented Lagrangian method used in optimization theory. To demonstrate the power of this approach for structure-variable systems, several applications are presented as e.g. a mechanical snake, an electronic power converter and the analysis of the curve squealing of trains.

Type of Seminar:
Public Seminar
Prof. Christoph Glocker
ETH Zurich, Inst. of Mechanical Systems
Jun 07, 2006   17:15

ETH Zentrum, Gloriastr. 35, Building ETZ, Room E6
Contact Person:

Prof. Lino Guzzella
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Biographical Sketch:
09/72-06/81: Wittelsbacher Gymnasium München, humanistischer Zweig (secondary academic school emphasizing classical languages and cultures) 06/81: Abitur (general qualification for university entrance) 11/83-03/89: Academic education in mechanical engineering at Technical University of Munich 03/89: Diploma degree in engineering 04/89-06/95: Wissenschaftlicher Assistent (research assistant with educational duties) at Institute B of Mechanics, TU Munich 07/95: Doctor's degree in engineering 01/96-12/96: Feodor-Lynen fellowship of the Alexander von Humboldt foundation at the Institute of Steel Structures, Aristotle University of Thessaloniki, Greece 01/97-02/01: Akademischer Rat (senior lecturer) at Institute B of Mechanics, TU Munich 12/98: Offer of the Chair of Engineering Dynamics (full professorship) at Delft University of Technology 03/01-12/05: Extraordinarius for Mechanics at ETH Zurich 06/01: Certificate of Habilitation for Mechanics from TU Munich since 01/06: Ordinarius for Mechanics at ETH Zurich