# Symbolic-Numeric Integration of the Dynamical Cosserat Equations

## TL;DR

This paper introduces a symbolic-numeric method for integrating the dynamical Cosserat equations, improving computational efficiency in modeling slender structures like fibers and rods.

## Contribution

It combines symbolic and numerical techniques to solve the nonlinear PDE system of Cosserat equations, building on previous solutions for the kinematic part.

## Key findings

- The method effectively integrates the dynamical Cosserat equations.
- Experimental results show improved computational efficiency.
- Comparison with the generalized alpha-method validates the approach.

## Abstract

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized alpha-method illustrating the computational efficiency of our approach for problems in structural mechanics.