# Variational principles for nonlinear Kirchhoff rods

## TL;DR

This paper develops and clarifies variational principles for nonlinear Kirchhoff rods, highlighting the role of differential geometry and proposing simplified models for static and dynamic problems.

## Contribution

It systematically presents new and existing variational principles for nonlinear Kirchhoff rods, emphasizing geometric aspects and approximation methods.

## Key findings

- New variational principles for nonlinear Kirchhoff rods
- Clarification of geometric roles in rod modeling
- Identification of approximations for simplified formulations

## Abstract

The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented in a systematic way, helping to clarify certain aspects that have remained obscure. In particular, the study of transversely isotropic models reveals the delicate role that differential geometry plays in their formulation and unveils consequently some approximations that can be made to obtain simplified formulations.