Under CopyrightLinn, J.J.LinnHermansson, T.T.HermanssonAndersson, F.F.AnderssonSchneider, FabioFabioSchneider2022-03-1324.9.20192017https://publica.fraunhofer.de/handle/publica/39904910.24406/publica-fhg-399049The theory of Cosserat rods provides a self consistent framework for modeling large spatial deformations of slender flexible structures at small local strains. Discrete Cosserat rod models [1, 2] based on geometric finite differences preserve essential properties of the continuum theory. The present work investigates kinetic aspects of discrete quaternionic Cosserat rods defined on a staggered grid within the framework of Lagrangian mechanics. Assuming hyperelastic constitutive behaviour, the Euler-Lagrange equations of the model are shown to be equivalent to the (semi)discrete balance equations of forces, moments and inertial terms obtained from a direct discretization of the continuous balance equations via spatial finite differences along the centerline curve. Therefore, equilibrium configurations obtained by energy minimization correspond to solutions of the quasi-static balance equations. We illustrate this approach by two academic examples (Euler's Elastica and Kirchhoff's helix) and highlight its utility for practical applications with a use case from automotive industry (analysis of the layout of cooling hoses in the engine compartment of a passenger car).en003006519conference paper