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UID:20260601T025825EDT-1713oVw3OU@132.216.98.100
DTSTAMP:20260601T065825Z
DESCRIPTION:Title: Importance and effectiveness of representing the shapes 
 of Cosserat rods and framed curves as paths in the special Euclidean algeb
 ra.\n\n \n\nAbstract: We discuss how the shape of a special Cosserat rod c
 an be represented as a path in the special Euclidean algebra. By shape we 
 mean all those geometric features that are invariant under isometries of t
 he three-dimensional ambient space. The representation of the shape as a p
 ath in the special Euclidean algebra is intrinsic to the description of th
 e mechanical properties of a rod\, since it is given directly in terms of 
 the strain fields that stimulate the elastic response of special Cosserat 
 rods. Moreover\, such a representation leads naturally to discretization s
 chemes that avoid the need for the expensive reconstruction of the strains
  from the discretized placement and for interpolation procedures which int
 roduce some arbitrariness in popular numerical schemes. Given the shape of
  a rod and the positioning of one of its cross sections\, the full placeme
 nt in the ambient space can be uniquely reconstructed and described by mea
 ns of a base curve endowed with a material frame. By viewing a geometric c
 urve as a rod with degenerate point-like cross sections\, we highlight the
  essential difference between rods and framed curves\, and clarify why the
  family of relatively parallel adapted frames is not suitable for describi
 ng the mechanics of rods but is the appropriate tool for dealing with the 
 geometry of curves. (This is joint work with Giulio Giusteri.)\n
DTSTART:20170911T200000Z
DTEND:20170911T210000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Eliot Fried (Okinawa Institute of Science and Technology)
URL:/mathstat/channels/event/eliot-fried-okinawa-insti
 tute-science-and-technology-269948
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