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 -