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05/05/2011, 16:30 — 17:30 — Amphitheatre Pa1, Mathematics Building

Tudor Ratiu, *École Polytechnique Fédérale de Lausanne*

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The geometry of the equations of motion in continuum mechanics

I plan to link the basic equations appearing in rigid body dynamics, fluid mechanics, elasticity, and liquid crystals to reduction theory of Lagrangian systems with symmetry. One of the goals is to compare the equations appearing in the spatial and convective representations. A second goal is to show how this geometric approach leads to answers to some basic questions appearing in continuum mechanics. For example, it will be shown how to relate the Ericksen-Leslie director theory to the Eringen micropolar approach to the equations of motion for liquid crystals, a problem that has been open for the past thirty years.