Publication detail
Use of the Gauss-Ostrogradsky theorem in the mechanics of rigid and flexible bodies and environments
POCHYLÝ, F. FIALOVÁ, S.
English title
Use of the Gauss-Ostrogradsky theorem in the mechanics of rigid and flexible bodies and environments
Type
conference paper
Language
en
Original abstract
New relations for the calculation of static moments and moments of inertia used in the mechanics of rigid bodies are presented in the work. Using the Gauss-Ostrogradsky theorem, it is possible to determine these values not by the integration over a volume, but over the surface of a body. This is especially advantageous in numerical methods. The next part of the work is focused on the Gauss-Ostrogradsky theorem use in the dynamics of fluids, elastic bodies and magnetic fields. Non-stationary terms, such as local acceleration or time change of magnetic induction, are expressed by presented mathematical model so that their effects in the field V can be expressed by their acting equivalent interpreted over the surface S surrounding the surface of the body. Presented article also points to the possibility of using the Gauss-Ostrogradsky theorem in the interaction of bodies with a fluid, such as bodies with cavities filled with a fluid, that can be produced thanks to the use of modern 3D printing technologies. The article brings the presentation of new mathematical models, including their proofs.
English abstract
New relations for the calculation of static moments and moments of inertia used in the mechanics of rigid bodies are presented in the work. Using the Gauss-Ostrogradsky theorem, it is possible to determine these values not by the integration over a volume, but over the surface of a body. This is especially advantageous in numerical methods. The next part of the work is focused on the Gauss-Ostrogradsky theorem use in the dynamics of fluids, elastic bodies and magnetic fields. Non-stationary terms, such as local acceleration or time change of magnetic induction, are expressed by presented mathematical model so that their effects in the field V can be expressed by their acting equivalent interpreted over the surface S surrounding the surface of the body. Presented article also points to the possibility of using the Gauss-Ostrogradsky theorem in the interaction of bodies with a fluid, such as bodies with cavities filled with a fluid, that can be produced thanks to the use of modern 3D printing technologies. The article brings the presentation of new mathematical models, including their proofs.
Keywords in English
Gauss-Ostrogradsky theorem
Released
14.02.2023
Publisher
AIP Publishing
ISBN
978-0-7354-4325-9
Book
39th Meeting of Departments of Fluid Mechanics and Thermodynamics
Edition number
2672, 020016 (2023)
Pages from–to
1–6
Pages count
6
BIBTEX
@inproceedings{BUT182994,
author="Edita {Mariánková} and František {Pochylý} and Simona {Fialová},
title="Use of the Gauss-Ostrogradsky theorem in the mechanics of rigid and flexible bodies and environments",
booktitle="39th Meeting of Departments of Fluid Mechanics and Thermodynamics",
year="2023",
month="February",
pages="1--6",
publisher="AIP Publishing",
isbn="978-0-7354-4325-9"
}