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SUMMARY:Lie group and homogeneous variational integrators and their applic
 ations to geometric optimal control theory - Melvin Leok\, University of C
 alifornia\, San Diego
DTSTART:20190718T130000Z
DTEND:20190718T140000Z
UID:TALK127399@talks.cam.ac.uk
CONTACT:Alberto Padoan
DESCRIPTION:The geometric approach to mechanics serves as the theoretical 
 underpinning of innovative control methodologies in geometric control theo
 ry. These techniques allow the attitude of satellites to be controlled usi
 ng changes in its shape\, as opposed to chemical propulsion\, and are the 
 basis for understanding the ability of a falling cat to always land on its
  feet\, even when released in an inverted orientation.  We will discuss th
 e application of geometric structure-preserving numerical schemes to the o
 ptimal control of mechanical systems. In particular\, we consider Lie grou
 p variational integrators\, which are based on a discretization of Hamilto
 n's principle that preserves the Lie group structure of the configuration 
 space. In contrast to traditional Lie group integrators\, issues of equiva
 riance and order-of-accuracy are independent of the choice of retraction i
 n the variational formulation. The importance of simultaneously preserving
  the symplectic and Lie group properties is also demonstrated. Recent exte
 nsions to homogeneous spaces yield intrinsic methods for Hamiltonian flows
  on the sphere\, and have potential applications to the simulation of geom
 etrically exact rods\, structures and mechanisms. Extensions to Hamiltonia
 n PDEs and uncertainty propagation on Lie groups using noncommutative harm
 onic analysis techniques will also be discussed.
LOCATION:Cambridge University Engineering Department\, Lecture Theatre 1
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