References
Auffray N, dell’ Isola F, Eremeyev V, Madeo A, Rosi G (2015) Analytical continuum mechanics à la Hamilton-Piola: least action principle for second gradient continua and capillary fluids. Mech Math Solids (MMS) 20(4):375–417
Cattani C, De Maria M (1996) Geniality and rigor: the Einstein – Levi-Civita correspondence (1915–1917). Riv Stor Sci (2) 4(1):1–22; as cited in MacTutor archive
Dell’Aglio L (1993) Tradizioni di ricerca nella meccanica celeste classica: il problema dei tre corpi in Levi-Civita e Sundman [Research traditions in classical celestial mechanics: the three-body problem in Levi-Civita and Sundman]. Physis Rivista Internazionale di Storia della Scienza 30(1):105–144
Dell’Aglio L, Israel G (1989) La théorie de la stabilité et l’analyse qualitative des équations différentielles ordinaires dans les mathématiques italiennes: le point de vue de Tullio Levi-Civita [The theory of stability and the qualitative analysis of ordinary differential equations in Italian mathematics: the point of view of Tullio Levi-Civita]. Cahiers du Séminaire d’histoire des Mathématiques 10:283–321
dell’Isola F, Maier G, Perego U, Andreaus U, Esposito R, Forest S (2014) The complete works of Gabrio Piola, vol I. Springer, Cham
dell’Isola F, Della Corte A, Esposito R, Russo L (2016) Some cases of unrecognized transmission of scientific knowledge: from antiquity to Gabrio Piola’s peridynamics and generalized continuum theories. In: Generalized continua as models for classical and advanced materials. Volume 42 of the series advanced structured materials, Springer, Cham, pp 77–128
dell’Isola F, Andreaus U, Cazzani A, Esposito R, Placidi L, Perego U, Maier G, Seppecher P (2019) The complete works of gabrio piola, vol II. Springer, Cham
Germain P (1973) The method of virtual power in continuum mechanics. Part 2: microstructure. SIAM J Appl Math 25(3):556–575
Israel G (2010) Il fascismo e la razza: la scienza italiana e le politiche razziali del regime, Il mulino
Lebedev LP, Cloud MJ, Eremeyev VA (2010) Tensor analysis with applications in mechanics. World Scientific, Singapore
Levi-Civita T (1893) Sugli infiniti ed infinitesimi attuali quali elementi analitici [On the actual infinite and infinitesimal as analytical elements]. Atti del R. Istituto veneto di scienze, lettere ed arti, vol LI, pp 1765–1815
Levi-Civita T (1893–1894) Sugli invarianti assoluti [On absolute invariants]. Atti del R Istituto veneto di scienze lettere ed arti s 7, pp 1447–1523
Levi-Civita T (1895) I gruppi di operazioni funzionali e l’inversione degli integrali definiti [Groups of functional operations and the inversion of definite integrals]. Rend. del R. Istituto lombardo di scienze e lettere, s 2, 28:529–544; 565–577
Levi-Civita T (1896) Sulle trasformazioni delle equazioni dinamiche [On the transformations of dynamic equations]. Annali di matematica pura ed applicata s 2, 24:255–300
Levi-Civita T (1899) Tipi di potenziali che si possono far dipendere da due sole coordinate [Types of potentials that can be made dependent on only two coordinates]. Mem. dell’Accademia delle scienze di Torino, s. 2, XLIX:105–152
Levi-Civita T (1901) Sopra alcuni criteri di instabilità [On some criteria of instability]. Annali di matematica pura ed applicata s 3, 5:221–308
Levi-Civita T (1903) Condition du choc dans le problème restreint des trois corps [Collision condition in the restricted three-body problem]. Comptes-rendus de the Académie des sciences de Paris CXXXVI: 221–223
Levi-Civita T (1904) Traiettorie singolari ed urti nel problema ristretto dei tre corpi [Singular trajectories and collisions in the restricted three-body problem]. Annali di matematica pura ed applicata s 3, 9:1–32
Levi-Civita T (1906) Sur la recherche des solutions particulières des systèmes différentiels et sur les mouvements stationnaires [On the search of particular solutions to differential systems and on stationary motions]. Prace matematyczno-fizyczne (Warszawa) 17:1–40
Levi-Civita T (1907a) Scie e leggi di resistenza [Contrails and laws of resistance]. Rend del Circolo matematico di Palermo XXIII:1–37
Levi-Civita T (1907b) Sulla massa elettromagnetica [On the electromagnetic mass]. Il Nuovo Cimento s 5, 14:271–304
Levi-Civita T (1909) Sulla forma dell’anello di Saturno [On the shape of the ring of Saturn]. Atti del R Istituto veneto di scienze lettere ed arti LXVIII:557–583
Levi-Civita T (1915) Sulla regolarizzazione del problema piano dei tre corpi [On the regularization of the plane three-body problem]. Atti della R. Accademia dei Lincei. Rendiconti cl di scienze fisiche matem e natur s 5 XXIV:61–75
Levi-Civita T (1916) Sopra due trasformazioni canoniche desunte dal moto parabolico [On two canonical transformations deduced from parabolic motion]. Atti della R Accademia dei Lincei Rendiconti cl di scienze fisiche matem e natur s 5, XXV:446–458
Levi-Civita T (1917a) Nozione di parallelismo in una varietà qualunque e conseguente specificazione geometrica della curvatura riemanniana [Notion of parallelism in any variety and consequent geometric specification of the Riemannian curvature]. Rendiconti del Circolo Matematico di Palermo (in Italian) 42:173–205. https://doi.org/10.1007/BF03014898. JFM 46.1125.02
Levi-Civita T (1917b) Statica einsteiniana [Einsteinian statics]. Atti della R. Accademia dei Lincei. Rendiconti cl di scienze fisiche matem e natur s 5, XXVI, 1:458–470
Levi-Civita T (1918a) Sur la régularisation du problème des trois corps [On the regularization of the three-body problem]. Acta Math XLII:99–144
Levi-Civita T (1918–1919) Come potrebbe un conservatore giungere alle soglie della nuova meccanica [How a conservative could reach the thresholds of new mechanics]. Rend del Seminario matematico dell’Università di Roma V:10–28
Levi-Civita T (1918b) ds 2 einsteiniani in campi newtoniani [Einsteinian ds 2 in Newtonian fields]. Atti della R. Accademia dei Lincei. Rendiconti cl di scienze fisiche matem e natur 2:307–317; XXVII (1918), s 1, pp 3–12; s 2, pp 183–191, 220–229, 240–248, 283–292, 343–351; vol XXVIII (1919), s 1, pp 3–13, 101–109
Levi-Civita T (1924) Questioni di meccanica classica e relativistica [Issues of classical and relativistic mechanics], Bologna
Levi-Civita T (1925a) Détermination rigoureuse des ondes permanentes d’ampleur finie [Rigorous determination of permanent waves of finite magnitude]. Math Ann XCIII:264–314
Levi-Civita T (1925b) Lezioni di calcolo differenziale assoluto [Lectures of absolute differential calculus]. Roma. The absolute differential calculus (London & Glasgow, Blackie & Son 1927) (edited by Enrico Persico, trans. by Marjorie Long)
Levi-Civita T (1926) Sur l’écart géodésique [On the geodesic gap]. Math Ann XCVII:291–320
Levi-Civita T (1928a) Sugli invarianti adiabatici [On adiabatic invariants]. Atti del Congresso internazionale dei fisici, Como 1927, I–II, Bologna, pp 475–513
Levi-Civita T (1928b) Fondamenti di meccanica relativistica [Fundamentals of relativistic mechanics], Bologna
Levi-Civita T (1931a) Rifrazione e riflessione nella relatività generale [Refraction and reflection in general relativity]. Atti della Pontificia Accademia delle scienze LXXXIV:332–352
Levi-Civita T (1931b) Caratteristiche dei sistemi differenziali e propagazione ondosa [Characteristics of differential systems and wave propagation], Bologna
Levi-Civita T (1934) Some mathematical aspects of the new mechanics. Bull Am Math Soc XXXIX:535–563
Levi-Civita T (1937) The relativistic problem of several bodies. Am J Math IL:9–22
Levi-Civita T (1950) Le problème des n corps en relativité générale [The problem of n bodies in general relativity], Paris, posthumous
Levi-Civita T, Amaldi U (1923) Lezioni di meccanica razionale [Lectures of rational mechanics] I, Bologna II, ibid. [1926–1927]
Lichnerowicz A (1946–1987) Eléments de calcul tensoriel. No. BOOK. Jacques Gabay
Mazliak L, Tazzioli R (2009) Mathematicians at War. Volterra and his french colleagues in World War I. Springer, Dordrecht
Nastasi P, Tazzioli R (2005) Toward a scientific and personal biography of Tullio Levi-Civita (1873–1941). Hist Math 32(2):203–236
Nastasi P, Tazzioli R (2013) I matematici italiani e l’internazionalismo scientifico (1914–1924). La Matematica nella Società e nella Cultura. Rivista dell’Unione Matematica Italiana 6(1):355–405
Poincaré H (1890) Sur le problème des trois corps et les équations de la dynamique [The the three-body problem and the equations of dynamics]. Acta Math 13(1):A3–A270
Ricci G, Levi-Civita T (1900) Méthodes de calcul différentiel absolu et leurs applications [Methods of differential absolute calculus and their applications]. Mathematische Annalen LIV:125–201
Sundman KF (1909) Nouvelles recherches sur le problème des trois corps [New researches on the three-body problem]. Acta Societatis Scientiarum Fennicae 35: 1–27
Truesdell C, Noll W (2013) The Non-Linear Field Theories of Mechanics/Die Nicht-Linearen Feldtheorien der Mechanik, vol 2. Springer Science & Business Media, Berlin
Truesdell C, Toupin R (1960) The classical field theories. Principles of classical mechanics and field theory/Prinzipien der Klassischen Mechanik und Feldtheorie. Springer, Berlin/Heidelberg, pp 226–858
Weinstein G (2012) Einstein the stubborn: correspondence between Einstein and Levi-Civita. arXiv preprint arXiv:1202.4305
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dell’Isola, F., Barchiesi, E., Placidi, L. (2019). Levi-Civita, Tullio. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_297-1
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