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CATEGORIES:Cambridge Centre for Analysis talks
SUMMARY:Geometric Mechanics &\; Symmetry: From Finite t
o Infinite Dimensions short course - day 3 - Profe
ssor D.D.Holm\, Imperial College London
DTSTART;TZID=Europe/London:20130529T150000
DTEND;TZID=Europe/London:20130529T170000
UID:TALK43955AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/43955
DESCRIPTION:Classical mechanics\, one of the oldest branches o
f science\, has undergone a long evolution\, devel
oping hand in hand with many areas of mathematics\
, including calculus\, differential geometry\, and
the theory of Lie groups and Lie algebras. The mo
dern formations of Lagrangian and Hamiltonian mech
anics\, in the coordinate-free language of differe
ntial geometry\, are elegant and general. They pro
vide a unifying framework for many seemingly dispa
rate physical systems\, such as n-particle systems
\, rigid bodies and other continua\, and electroma
gnetic and quantum systems.\n\nThis short course o
n Geometric Mechanics and Symmetry is a friendly a
nd fast-paced introduction to the geometric approa
ch to classical mechanics\, suitable for PhD stude
nts or advanced undergraduates. It fills a gap bet
ween traditional classical mechanics texts and adv
anced modern mathematical treatments of the subjec
t. After a summary of the setting of mechanics usi
ng calculus on smooth manifolds and basic Lie grou
p theory illustrated in matrix multiplication\, th
e rest of the course considers how symmetry reduct
ion of Hamilton's principle allows one to derive a
nd analyse the Euler-PoincarĂ© equations for dynami
cs on Lie groups. The main topics are solitons in
shallow water waves\, ideal incompressible fluid d
ynamics and geophysical fluid dynamics (GFD).\n\nT
hree worked examples that illustrate the course ma
terial in simpler settings are given full detail i
n the course notes. These will be assigned as outs
ide reading and then discussed in Q&A sessions in
class.
LOCATION:MR14
CONTACT:CCA
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