Annali di Matematica Pura ed Applicata

, Volume 106, Issue 1, pp 315–327 | Cite as

Two variational principles for second order materials within general relativity

  • Mario Pitteri


Two variational principles for second order materials are stated in general relativity; the gravitation equations implied by the first variational principle are proved to be compatible with the conservation equations derived from the second one in that all these equations involve the same total energy tensor. The terms of this tensor have a Lagrangian definition, hence a priori they seem to depend on the choice of the reference configuration; we prove that this is not the case.


Total Energy General Relativity Variational Principle Conservation Equation Reference Configuration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    V. L. Berdichewski,Costruzione di modelli di sistemi continui attraverso un principio variazionale, PMM (Mat. e Mecc. Applicata, Mosca),30 (1966), p. 510.Google Scholar
  2. [2]
    A. Bressan,Relativistic theories of materials, being printed by Springer.Google Scholar
  3. [3]
    A. Bressan,Cinematica dei sistemi continui in relatività generale, Ann. Mat. Pura o Applicata,62 (1963), p. 99.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    A. Bressan,Elasticità relativistica con coppie di contatto, Ricerche di Matematica,15 (1966), p. 169.zbMATHGoogle Scholar
  5. [5]
    A. Bressan,Coppie di contatto in relatività, Ann. Scuola Normale Sup. di Pisa,20 (1966), p. 63.zbMATHMathSciNetGoogle Scholar
  6. [6]
    A. Bressan,Elasticità con elettromagnetostrizione, Ann. di matematica Pura e Applicata,74 (1966), p. 383.MathSciNetGoogle Scholar
  7. [7]
    A. Bressan,Sistemi polari in relatività, Symposia Matematica (Ist. Naz. di Alta Mat.),1 (1968), p. 289.Google Scholar
  8. [8]
    A. Bressan,Principi variazionali relativistici in presenza di coppie di contatto, Ann. Mat. Pura e Applicata,94 (1972), p. 201.zbMATHMathSciNetGoogle Scholar
  9. [9]
    H. G. Schopf,Allgemeinrelativistische Prinzipien der Kontinuums-mechanik, Ann. Physik.12 (1964), p. 377.MathSciNetGoogle Scholar
  10. [10]
    C. Truesdell - R. Toupin,The classical field theories, in Handbuch der Physik, vol. 3 (1960).Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Mario Pitteri
    • 1
  1. 1.Padova

Personalised recommendations