Symetry methods in geometrics mechanics - Tudor Ratiu

[Pawamoy]

Author: Tudor Ratiu
Institution: Section de Mathematiques, Faculté des Sciences de Base EPFL, Lausanne, Switzerland
Website: http://cag.epfl.ch/page-39504-en.html
Video: http://www.youtube.com/watch?v=Dwk4U9jrGPM
Slides: Ratiu_symmetry methods.pdf
Presentation: https://www.see.asso.fr/node/14276
Creative Commons Attribution-ShareAlike 4.0 International

Abstract:
The goal of these lectures is to show the influence of symmetry in various aspects of theoretical mechanics. Canonical actions of Lie groups on Poisson manifolds often give rise to conservation laws, encoded in modern language by the concept of momentum maps. Reduction methods lead to a deeper understanding of the dynamics of mechanical systems. Basic results in singular Hamiltonian reduction will be presented. The Lagrangian version of reduction and its associated variational principles will also be discussed. The understanding of symmetric bifurcation phenomena in for Hamiltonian systems are based on these reduction techniques. Time permitting, discrete versions of these geometric methods will also be discussed in the context of examples from elasticity.

References

• Demoures, F., Gay-Balmaz, F., Ratiu, T.S.: Multisymplectic variational integrators and space/time symplecticity, Communications in Analysis and Applications (2015), to appear
• Gay-Balmaz, F., Ratiu, T.S.: The geometric structure of complex fluids, Advances in Applied Mathematics, 42 (2009), 176--275
• Gay-Balmaz, F., Marsden, J.E., Ratiu, T.S.: Reduced variational formulations in free boundary continuum mechanics, Journ. Nonlinear Sci., 22 (2012), 463-497
• Libermann, P., Marle, C.-M.: Symplectic Geometry and Analytical Mechanics. Symplectic Geometry and Analytical Mechanics. D. Reidel Publishing Company, Dordrecht (1987)
• Marsden, J.E, Ratiu, T.S.: Introduction to Mechanics and Symmetry, Texts in Applied Mathematics 17, second edition, Springer Verlag, (1998)
• Marsden, J.E, Misiolek, G., Ortega, J.-P., Perlmutter, M., Ratiu, T.S.: Hamiltonian Reduction by Stages, Springer Lecture Notes in Mathematics, 1913, Springer-Verlag, New York (2007)
• Marsden J.E, West M.: Discrete mechanics and variational integrators, Acta Numer., 10 (2001), 357–514.
• Ortega, J.-P., Ratiu, T.S.: Momentum Maps and Hamiltonian Reduction, Progress in Mathematics 222, Birkh"auser, Boston (2004)

Bio:

• BA in Mathematics, University of Timisoara, Romania, 1973
• MA in Applied Mathematics, University of Timisoara, Romania, 1974
• Ph.D. in Mathematics, University of California, Berkeley, 1980
• T.H. Hildebrandt Research Assistant Professor, University of Michigan, Ann Arbor, USA 1980-1983
• Associate Professor of Mathematics, University of Arizona, Tuscon, USA 1983-1988
• Professor of Mathematics, University of California, Santa Cruz, USA, 1988-2001
• Chaired Professor of Mathematics, Ecole Polytechnique Federale de Lausanne, Switzerland, 1998 - present
• Professor of Mathematics, Skolkovo Institute of Science and Technonology, Moscow, Russia, 2014 - present