Abstract
In the past, the term ‘mathematical physics’ had substantially two meanings. On one hand, it simply indicated modern physics, which considered mathematics its own language; in this sense, Galileo, Newton, Kepler, etc., were distinguished mathematical physicists. On the other hand, it pointed to the branch of science that developed in the XIX century and had enabled the solution of some specific problems governed by partial differential equations, such as, for instance, heat propagation, potential theory, theory of elasticity; in this sense Fourier, Lamé, Gauss, Piola, Beltrami, etc., stood among the most important mathematical physicists. Today the term indicates an academic discipline, practiced by mathematicians, having some principles of physical nature at its basis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Barbin E, Guitart R (2013) Mathematical physics in the style of Gabriel Lamé and the treatise of Emile Mathieu. In: Barbin E, Pisano R (eds) (2013) The dialectic relation between physics and mathematics in the XIXth century. Springer, Dordrecht
Capecchi D (2012) History of virtual work laws. A history of mechanical prospective. Springer, Milan
Capecchi D, Ruta G, Tazzioli R (2006) Enrico Betti: Teoria del potenziale. Hevelius, Benevento
Capecchi D, Ruta G (2011) La scienza delle costruzioni in Italia nell’Ottocento. Un’analisi storica dei fondamenti della scienza delle costruzuoni. Springer, Milan
Carnot L (1803) Principes fondamentaux de l’équilibre et du mouvement. Deterville, Paris
Cauchy AL (1827) De la pression ou tension dans un corps solides. In: Cauchy AL (1882-1974) Oeuvres complètes, (27 vols). Gauthier-Villars, Paris, s II, vol 7, pp 60-81
Corbini A (2006) La teoria della scienza nel XIII secolo. I commenti agli analitici secondi. Edizioni del Galluzzo, Firenze
Euler L (1752) Découverte d’un nouveau principe de mécanique (1750). Mémoires de l’académie des sciences de Berlin 6:185-217
Euler L (1761) Principia motus fluidorum (1753). Novi Commentari Academiae Petropolitanae, vol. 6. pp. 271-311
Fourier J (1822) Théorie analytique de la chaleur. Firmin-Didot, Paris
Gauss CF (1840) Allgemeine Lehrsätze in Beziehung auf die im verkehrten Verhältnisse wirkenden Anziehungs- und Abstossungskräfte. In Gauss CF (1863-1933) Werke. Göttingen, vol. 5, pp. 194-242
Green G (1828) An essay of the application of the mathematical analysis to the theories of electricity and Magnetism. In: Green G (1871) Mathematical papers of the late George Green. McMillan and co., London, pp. 1–82
Green G (1835) On the determination of the exterior and interior attractions of ellipsoids of variable densities. In: Green G (1871) Mathematical papers of the late George Green. McMillan and co., London, pp. 187–222
Hilbert D (1904) Über das Dirichletsche Prinzip. Mathematische Annalen, 59: 161–186
Hilbert D (1905) Über das Dirichletsche Prinzip. Journal für die reine und angewandte Mathematik, 129: 63–67
Kline M (1972) Mathematical thought from ancient to modern times. Oxford University Press, Oxford
Lagrange JL (1780) Theorie de la libration de la Lune. In: Lagrange JL (1867-1892) Oeuvres de Lagrange. Serret JA, [Darboux G] (eds). Gauthier-Villars, Paris, vol 5, pp 5-124
Lagrange JL (1788) Méchanique analitique, Desaint, Paris. Anastatic copy (1989). Jacques Gabay, Paris
Lagrange JL (1811) Mécanique analytique (tome premier). In: Lagrange JL (11867-1892) Oeuvres de Lagrange. Serret JA, [Darboux G] (eds). Gauthier-Villars, Paris, vol 11
Lagrange JL (1815) Mécanique analytique (tome second). In: Lagrange JL (11867-1892) Oeuvres de Lagrange. Serret JA, [Darboux G] (eds). Gauthier-Villars, Paris, vol 12
Lamé G (1852) Leçons sur la théorie mathematique de l’élasticité des corps solides. Bachelier, Paris
Lamé G (1857) Leçons sur les fonctions inverses des transcendantes et les surfaces isotherme. Mallet-Bachelier, Paris
Lamé G (1861) Leçons sur la théorie analytique de la chaleur. Mallet-Bachelier, Paris
Lamé G (1859) Leçons sur les coordonnées curvilignes et leurs diverses applications. Mallet-Bachelier, Paris
Lamé G (1863) Note sur la marche á suivre pour découvrir le principe seul véritablement universel de la nature physique. Comptes rendus de l’Académie des sciences 56: 983-989
Laplace P S (1785) Théorie des attractions des sphéro’ides et de la figure des planétes. Mémoires de l’Académie des sciences de Paris (1782), pp. 113-196
Laplace P S (1829/an VII) Traité de mécanique céléste, vol.1. Duprat, Paris
Laplace P S (1785)Théorie des attractions des sphéro’ides et de la figure des planétes. Mémoires de l’Académie des sciences de Paris (1782), pp. 113-196
Lennox JG (1985) Aristotle, Galileo and the Mixed Sciences. In Reinterpreting Galileo, ed. William Wallace, Washington D.C, pp. 29-51.
Piola G (1825b) Sull’applicazione de’ principj della meccanica analitica del Lagrange ai principali problemi. Regia Stamperia, Milano
Piola G (1832) La meccanica de’ corpi naturalmente estesi trattata col calcolo delle variazioni. Opuscoli matematici e fisici di diversi autori. Giusti, Milano, Vol. 1, pp. 201–236. See also Piola G (1833) La meccanica de’ corpi naturalmente estesi trattata col calcolo delle variazioni. Giusti, Milano
Piola G (1836) Nuova analisi per tutte le questioni della meccanica molecolare. Memorie di matematica e fisica della Società italiana delle scienze, vol 21, pp. 155–321
Piola G (1848) Intorno alle equazioni fondamentali del movimento di corpi qualsivogliono considerati secondo la naturale loro formae costituzione. Memorie di matematica e fisica della Società italiana delle scienze, vol 24, pp. 1–186. Translated in this volume
Piola G (1856) Di un principio controverso della Meccanica Analitica di Lagrange e delle sue molteplici applicazioni. Memorie dell’Istituto Lombardo, vol 6, pp. 389–496. Translated in this volume.
Pisano R, Capecchi D (2009) La théorie analytique de la chaleur. Notes on Fourier and Lamé. Sabix, 44: 87-93
Poisson SD (1813) Rémarques sur une équation qui se présente dans la théorie des attractions des sphéro’ides. Nouveau Bulletin de la Sociétᅵé Philomatique de Paris 3: 388-392
Poisson SD (1829) Mémoire sur l’équilibre et le mouvement des corps élastiques. Mémoires de l’Académie des sciences de l’Institut de France, vol 8, pp 357–570
Weierstrass K (1895) Über die sogenannte Dirichlet’sche Princip. In: Mathematische Werke, 7 voll., 1894-1927, Berlin, vol. 2, pp. 49-54.
Schlote KH (2013) The emergence of mathematical physics at the university of Leipzig. In: Barbin E, Pisano R (eds) (2013) The dialectic relation between physics and mathematics in the XIXth century. Springer, Dordrecht
Tarantino P (2012) La trattazione aristotelica delle scienze subordinate negli Analitici secondi. Rivista di storia della losoafia 3:445-469
Tazzioli R (2001) Green’s function in some contributions of 19th century mathematicians. Historia Mathematica 28: 232-252
Truesdell CA (1968) Essay in the history of mechanics. Spinger, New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Capecchi, D. (2014). Gabrio Piola and Mathematical Physics. In: dell'Isola, F., Maier, G., Perego, U., Andreaus, U., Esposito, R., Forest, S. (eds) The complete works of Gabrio Piola: Volume I. Advanced Structured Materials, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-00263-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-00263-7_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00262-0
Online ISBN: 978-3-319-00263-7
eBook Packages: EngineeringEngineering (R0)