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.
CITATION STYLE
Boyer, F., & Renda, F. (2015). Poincaré equations for cosserat shells: Application to cephalopod locomotion. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 511–518). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_55
Mendeley helps you to discover research relevant for your work.