Lagrangian field theory in space and time for geometrically exact Cosserat rods - Lang, Holger; Linn, Joachim (2009)
In this article, we derive the balance of linear and angular momentum equations for geometrically exact Cosserat rods from a two dimensional Lagrangian field approach in space and time. As we use a full quaternion description for the rotatory part of the balance equations, they constitute a system of nonlinear hyperbolic partial differential algebraic equations. We prove their equivalence to the classical Euclidean frame description.
Keywords: Cosserat rods; Geometrically exact rods; Small strains; Large deformations; Deformable bodies; Lagrangian field theory; Calculus of variations; Partial differential algebraic equations