TY - GEN
T1 - Poincaré equations for cosserat shells
T2 - 2nd International Conference on Geometric Science of Information, GSI 2015
AU - Boyer, Frederic
AU - Renda, Federico
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - In 1901 Henri Poincaré proposed a new set of equations for mechanics. These equations are a generalization of Lagrange equations to a system whose configuration space is a Lie group, which is not necessarily commutative. Since then, this result has been extensively refined by the Lagrangian reduction theory. In this article, we show the relations between these equations and continuous Cosserat media, i.e. media for which the conventional model of point particle is replaced by a rigid body of small volume named microstructure. In particular, we will see that the usual shell balance equations of nonlinear structural dynamics can be easily derived from the Poincaré’s result. This framework is illustrated through the simulation of a simplified model of cephalopod swimming.
AB - In 1901 Henri Poincaré proposed a new set of equations for mechanics. These equations are a generalization of Lagrange equations to a system whose configuration space is a Lie group, which is not necessarily commutative. Since then, this result has been extensively refined by the Lagrangian reduction theory. In this article, we show the relations between these equations and continuous Cosserat media, i.e. media for which the conventional model of point particle is replaced by a rigid body of small volume named microstructure. In particular, we will see that the usual shell balance equations of nonlinear structural dynamics can be easily derived from the Poincaré’s result. This framework is illustrated through the simulation of a simplified model of cephalopod swimming.
UR - http://www.scopus.com/inward/record.url?scp=84950327334&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-25040-3_55
DO - 10.1007/978-3-319-25040-3_55
M3 - Conference contribution
AN - SCOPUS:84950327334
SN - 9783319250397
SN - 9783319250397
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 511
EP - 518
BT - Geometric Science of Information - 2nd International Conference, GSI 2015, Proceedings
A2 - Nielsen, Frank
A2 - Nielsen, Frank
A2 - Nielsen, Frank
A2 - Barbaresco, Frederic
A2 - Barbaresco, Frederic
A2 - Nielsen, Frank
PB - Springer Verlag
Y2 - 28 October 2015 through 30 October 2015
ER -