@article{Fiori2024, 
author = {Simone Fiori},
title = {Coordinate-free Lie-group-based modeling and simulation of a submersible vehicle},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {10157-10184},
keywords = {Lie group theory, Lie algebra, Coordinate-free mathematical model, submersible vehicle, Lagrange-d'Alembert principle, Euler-Poincaré equation, Lie-group integration, numerical simulation},
url = {https://www.sciopen.com/article/10.3934/math.2024497},
doi = {10.3934/math.2024497},
abstract = {Submersible vehicles may be regarded as complex systems because of their complex interaction with the surrounding fluid. This paper presents a mathematical model of a submersible vehicle formulated in a coordinate-free manner through the language of Lie groups and Lie algebras. The d'Alembert virtual-work principle was applied in conjunction with the minimal-action principle for a rigid body in order to incorporate into the mathematical model external influences such as fluid-current-induced deflection and control inputs. Such a method from mathematical physics can also take into consideration how a vehicle interacts with the fluid it is immersed in under the form of added (or virtual) mass. The resulting equations of motion were given over the Lie group of three-dimensional rotations as (non-pure) Euler-Poincaré relations. A numerical simulation technique based on Lie-group integrators was also briefly recalled and deployed to simulate the behavior of such mathematical model of an existing, academic-design-type submersible vehicle.}
}