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SUMMARY:Geometric Mechanics & Symmetry: From Finite to Infinite Dimensions
  short course - day 3 - Professor D.D.Holm\, Imperial College London
DTSTART:20130529T140000Z
DTEND:20130529T160000Z
UID:TALK43955@talks.cam.ac.uk
CONTACT:CCA
DESCRIPTION:Classical mechanics\, one of the oldest branches of science\, 
 has undergone a long evolution\, developing hand in hand with many areas o
 f mathematics\, including calculus\, differential geometry\, and the theor
 y of Lie groups and Lie algebras. The modern formations of Lagrangian and 
 Hamiltonian mechanics\, in the coordinate-free language of differential ge
 ometry\, are elegant and general. They provide a unifying framework for ma
 ny seemingly disparate physical systems\, such as n-particle systems\, rig
 id bodies and other continua\, and electromagnetic and quantum systems.\n\
 nThis short course on Geometric Mechanics and Symmetry is a friendly and f
 ast-paced introduction to the geometric approach to classical mechanics\, 
 suitable for PhD students or advanced undergraduates. It fills a gap betwe
 en traditional classical mechanics texts and advanced modern mathematical 
 treatments of the subject. After a summary of the setting of mechanics usi
 ng calculus on smooth manifolds and basic Lie group theory illustrated in 
 matrix multiplication\, the rest of the course considers how symmetry redu
 ction of Hamilton's principle allows one to derive and analyse the Euler-P
 oincaré equations for dynamics on Lie groups. The main topics are soliton
 s in shallow water waves\, ideal incompressible fluid dynamics and geophys
 ical fluid dynamics (GFD).\n\nThree worked examples that illustrate the co
 urse material in simpler settings are given full detail in the course note
 s. These will be assigned as outside reading and then discussed in Q&A ses
 sions in class.
LOCATION:MR14
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