RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Dal'nevost. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Dal'nevost. Mat. Zh., 2018, Volume 18, Number 2, Pages 150–176 (Mi dvmg377)  

Geometric formulations of the balance laws of continuum mechanics

A. I. Gudimenkoab

a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: The balance laws of classical continuum mechanics are formulated in terms of differential forms (mass balance) and vector-valued differential forms (balances of momentum and energy) on the trajectory of material continuum. The traditional formulations of the laws are obtained as a consequence of the proposed formulations. Balance equations are written in a form suitable for an arbitrary observer. The formulation of the equation of motion of an ideal fluid in terms of differential forms is derived from the proposed formulations.

Key words: conservation laws, vector-valued forms, reference frames.

Full text: PDF file (725 kB)
References: PDF file   HTML file
UDC: 539.3 514
MSC: Primary 74A05; Secondary 53B50
Received: 28.03.2018

Citation: A. I. Gudimenko, “Geometric formulations of the balance laws of continuum mechanics”, Dal'nevost. Mat. Zh., 18:2 (2018), 150–176

Citation in format AMSBIB
\Bibitem{Gud18}
\by A.~I.~Gudimenko
\paper Geometric formulations of the balance laws of continuum mechanics
\jour Dal'nevost. Mat. Zh.
\yr 2018
\vol 18
\issue 2
\pages 150--176
\mathnet{http://mi.mathnet.ru/dvmg377}


Linking options:
  • http://mi.mathnet.ru/eng/dvmg377
  • http://mi.mathnet.ru/eng/dvmg/v18/i2/p150

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Дальневосточный математический журнал
    Number of views:
    This page:55
    Full text:17
    References:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019