Abstract
Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers and are the main tool for the axiomatization of physical theories.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Arnold, V.I., Mathematical Methods of Classical Mechanics, Springer, 2nd edition, May 16, 1989.
Benvenuto, E., La scienza delle costruzioni e il suo sviluppo storico, Sansoni, Firenze, 1981.
Berdichevsky V., Variational Principles of Continuum Mechanics, Springer, 2009.
Bourdin, B., Francfort, G.A., Marigo, J.-J., The variational approach to fracture, J. Elasticity, 91, 1–3, 1–148, 2008. (The paper also appeared as a Springer book: ISBN: 978-1-4020-6394-7).
Colonnetti, G., Scienza delle costruzioni, Torino, Edizioni scientifiche Einaudi, 3rd ed., 1953–57.
Cosserat, E., Cosserat, F., Sur la Théorie des Corps Déformables, Herman, Paris, 1909.
dell’Isola, F., Seppecher, P., The relationship between edge contact forces, double force and interstitial working allowed by the principle of virtual power, Comptes Rendus de l’Academie de Sciences — Serie IIb: Mecanique, Physique, Chimie, Astronomie, vol. 321, pp. 303–308, 1995.
dell’Isola, F., Seppecher, P., Edge Contact Forces and Quasi-Balanced Power, Meccanica, vol. 32, pp. 33–52, 1997.
dell’Isola, F., Madeo, A., Seppecher, P., Boundary Conditions in Porous Media: A Variational Approach, Int. Journal of Solids and Structures, Vol. 46, 3150–3164, 2009.
dell’Isola, F., Madeo, A., Seppecher, P., “Beyond Euler-Cauchy continua”. In this book.
Feynman, R.P., Leighton, R., Sands, M., The Feynman Lectures on Physics: The Definitive and Extended Edition, (Feynman, Leighton, Sands), 3 vv., Addison Wesley, Reading (MA) 2nd ed., 2005.
Francfort, G.A., The chapter in this book by Prof. Gilles Frankfort.
Germain, P., La méthode des puissances virtuelles en mécanique des milieux continus. Premi’ere partie. Théorie du second gradient, J. Mécanique, 12, 235–274, 1973.
Homer. The Iliad. Translated by Murray, A. T., Loeb Classical Library Volumes 1. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd., 1924.
Lagrange, J.L., Mécanique Analytique, Editions Jaques Gabay, Sceaux, 1788.
Lanczos, C., The Variational Principles of Mechanics. Toronto: University of Toronto, 1970.
Landau, L.D., Lifshitz, E.M., Quantum Mechanics: Non-Relativistic Theory. Vol. 3 (3rd ed.), Pergamon Press, 1977.
Moiseiwitsch, B.L., Variational Principles, Dover, 1966.
Netz, R., Noel., W., The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity’s Greatest Scientist, Da Capo press, 2009. See also the website http://www.archimedespalimpsest.org/
Rorres, C., Completing Book II of Archimedes’s On Floating Bodies, The mathematical intelligencer, 26,3. Pages 32–42, 2004.
Russo, L., The Forgotten Revolution, Springer Verlag, 2003.
Vailati, G., Il principio dei lavori virtuali da Aristotele a Erone d’Alessandria, Scritti (Bologna, Forni, 1987), vol. II, pp. 113–128. Atti della R. Accademia delle Scienze di Torino, vol. XXXII, adunanza del 13 giugno 1897, quaderno IG (091) 75 I–III. 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 CISM, Udine
About this chapter
Cite this chapter
dell’Isola, F., Placidi, L. (2011). Variational principles are a powerful tool also for formulating field theories. In: dell’Isola, F., Gavrilyuk, S. (eds) Variational Models and Methods in Solid and Fluid Mechanics. CISM Courses and Lectures, vol 535. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0983-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-7091-0983-0_1
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-0982-3
Online ISBN: 978-3-7091-0983-0
eBook Packages: EngineeringEngineering (R0)