Publication result detail

Use of the Gauss-Ostrogradsky theorem in the mechanics of rigid and flexible bodies and environments

POCHYLÝ, F.; FIALOVÁ, S.

Original Title

Use of the Gauss-Ostrogradsky theorem in the mechanics of rigid and flexible bodies and environments

English Title

Use of the Gauss-Ostrogradsky theorem in the mechanics of rigid and flexible bodies and environments

Type

Paper in proceedings (conference paper)

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

Gauss-Ostrogradsky theorem

Key words in English

Gauss-Ostrogradsky theorem

Authors

POCHYLÝ, F.; FIALOVÁ, S.

RIV year

2024

Released

14.02.2023

Publisher

AIP Publishing

ISBN

978-0-7354-4325-9

Book

39th Meeting of Departments of Fluid Mechanics and Thermodynamics

Edition

AIP Conference Proceedings

Pages from

1

Pages to

6

Pages count

6

URL

https://aip.scitation.org/doi/pdf/10.1063/5.0133903

BibTex

@inproceedings{BUT182994,
  author="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",
  series="AIP Conference Proceedings",
  number="2672, 020016 (2023)",
  pages="1--6",
  publisher="AIP Publishing",
  doi="10.1063/5.0133903",
  isbn="978-0-7354-4325-9",
  url="https://aip.scitation.org/doi/pdf/10.1063/5.0133903"
}