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Non-smooth Dynamics
Nicht-glatte Dynamik
Last Updated: 2026-02-05 15:41:37
Abstract
Inequality problems in dynamics, in particular friction and impact problems with discontinuities in velocity and acceleration. Mechanical models of unilateral contacts, friction, sprag clutches, pre-stressed springs. Formulation by set-valued maps as linear complementarity problems. Numerical time integration of the combined friction impact contact problem.
Objective
The lecture provides the students an introduction to modern methods for inequality problems in dynamics. The contents of the lecture are fitted to frictional contact problems in mechanics, but can be transferred to a large class of inequality problems in technical sciences. The purpose of the lecture is to acquaint the students with a consistent generalization of classical mechanics towards systems with discontinuities, and to make them familiar with inequalities treated as set-valued constitutive laws.
Content
1. Kinematik: Drehung, Geschwindigkeit, Beschleunigung, virtuelle Verschiebung. 2. Aufbau der Mechanik: Definition der Kraft, virtuelle Arbeit, innere und äussere Kräfte, Wechselwirkungsprinzip, Erstarrungsprinzip, mathematische Form des Freischneidens, Definition der idealen Bindung. 3. Starre Körper: Variationelle Form der Gleichgewichtsbedingungen, Systeme starrer Körper, Übergang auf Minimalkoordinaten. 4. Einfache generalisierte Kräfte: Generalisierte Kraftrichtungen, Kinematik der Kraftelemente, Kraftgesetze, Parallel- und Reihenschaltung. 5. Darstellung mengenwertiger Kraftgesetze: Normalkegel, proximale Punkte, exakte Regularisierung. Anwendung auf einseitige Kontakte und Coulomb-Reibgesetze. 6. Stossfreie und stossbehaftete Bewegung: Bewegungsgleichung, Stossgleichung, Newton-Stossgesetze, Diskussion von Mehrfachstössen, Kane's Paradoxon. 7. Numerische Behandlung: Lineares Komplementaritätsproblem (LCP), Zeitdiskretisierung nach Moreau, Kontaktproblem in lokalen Koordinaten als LCP.
Resources
Lecture Notes
Es gibt kein Vorlesungsskript. Den Studierenden wird empfohlen, eine eigene Mitschrift der Vorlesung anzufertigen. Ein Katalog mit Übungsaufgaben und den zugehörigen Musterlösungen wird ausgegeben.
General Information
- Language
- German
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- end-of-semester examination
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Nicht-glatte Dynamik |
|
5 h weekly |
Offered In
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Mechatronics (Focus Coordinator: Prof. Bradley Nelson To achieve the 20 credits for Focus Specialization Mechatronics, 151-0640-00L Studies on Mechatronics is compulsory.)
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Microsystems and Nanoscale Engineering (Focus Coordinator: Prof. Christofer Hierold)
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Manufacturing Science (Focus Coordinator: Prof. Konrad Wegener To achieve the required 20 credit points for the focus specialization you need to pass all 3 compulsory courses (HS/FS). The other 8 credit points can be achieved from the elective courses.)
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Design, Mechanics and Materials (Focus Coordinator: Prof. Dirk Mohr In order to achieve the required 20 credit points for the Focus Specialization Design, Mechanics and Material you are free to choose any of the courses offered within the focus and are encouraged to select among those recommended. If you wish to take one of the Master level courses, you must get approval from the lecturer.)
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Mechanics, Materials, Structures (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
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