Lagrangian field theory in space and time for geometrically exact Cosserat rods

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.

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