# Implementation of the Euler-Rodrigues formula to define the initial configuration of offshore systems lines

## Palavras-chave:

Euler-Rodrigues formula, DOOLINES, Offshore systems## Resumo

During the construction of structural models for computational analysis, various pieces of information

concerning the structure, including the initial spatial configuration, are provided. This configuration represents the

spatial arrangement of the structure at the beginning of the simulation. In DOOLINES, an object-oriented

framework that performs nonlinear dynamic analysis of mooring lines and offshore production systems in the time

domain, the initial configurations of risers, hoses, and mooring lines are generated using the catenary equation,

which considers only axial stiffness, despite the presence of other stiffnesses such as bending and torsional

stiffness, as observed in risers. Because the initial configuration may differ from the relaxed configuration, it can

lead to the development of internal loads, even at time zero of the simulation. Therefore, the algorithm must discern

the difference between the initial and relaxed configurations and compute the corresponding loads. One possible

strategy, known as the "assembly" approach, involves considering the line in its relaxed position and prescribing

movement at one of the supports to bring it to its actual position in the initial configuration. However, this approach

requires computational effort before the actual simulation of interest. In this study, we implement the Euler-

Rodrigues formula of rigid body rotation to calculate the internal forces resulting from the initial configuration,

thus replacing the "assembly" approach. Through analysis of reference examples, we demonstrate that the results

obtained by the two strategies are similar. Consequently, due to its lower computational requirements, the Euler-

Rodrigues formula serves as a suitable replacement for the "assembly" approach.