A new look at classical mechanics of constrained systems
Annales de l'I.H.P. Physique théorique, Volume 66 (1997) no. 1, p. 1-36
@article{AIHPA_1997__66_1_1_0,
     author = {Massa, Enrico and Pagani, Enrico},
     title = {A new look at classical mechanics of constrained systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {66},
     number = {1},
     year = {1997},
     pages = {1-36},
     zbl = {0878.70009},
     mrnumber = {1434114},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1997__66_1_1_0}
}
Massa, Enrico; Pagani, Enrico. A new look at classical mechanics of constrained systems. Annales de l'I.H.P. Physique théorique, Volume 66 (1997) no. 1, pp. 1-36. http://www.numdam.org/item/AIHPA_1997__66_1_1_0/

[1] J.L. Lagrange, Mécanique Analytique, (Veuve Desaint, Paris, 1788), in Œuvres de Lagrange, Gauthier-Villars, Paris, 1867-1892.

[2] V.I. Arnold, Mathematical Methods of Classical Mechanics, MIR, Moscow, 1975.

[3] T. Levi-Civita, U. Amaldi, Lezioni di Meccanica Razionale, Zanichelli, Bologna, 1984, first edition 1922, second edition 1929.

[4] K. Gauss, Uber ein neues allgemeines Grundgesetz der Mechanik, Crelle J. reine Math., Vol. 4, 1829, pp. 232.

[5] E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, (4th ed.), Cambridge University Press, Cambridge, 1959. | MR 103613 | Zbl 0049.40801

[6] G. Hamel, Theoretische Mechanik. Eine einheitliche Einfuhrung in die gesamte Mechanik, Springer-Verlag, Berlin, 1949. | MR 34137 | Zbl 0036.24301

[7] A. Sommerfeld, Mechanics, Lectures on Theoretical Physics, Vol. 1, Academic Press, New York, San Francisco, London, 1942. | Zbl 0048.41806

[8] D.J. Saunders, The Geometry of Jet Bundles, London Mathematical Society, Lecture Note Series 142, Cambridge University Press, 1989. | MR 989588 | Zbl 0665.58002

[9] M. Crampin, G.E. Prince and G. Thompson, A Geometrical Version of the Helmholtz Conditions in Time-Dependent Lagrangian Dynamics, J. Phys. A: Math. Gen., Vol. 17, 1984, pp. 1437-1447. | MR 748776 | Zbl 0545.58020

[10] F. Cantrijn, J.F. Cariñena, M. Crampin and L.A. Ibort, Reduction of Degenerate Lagrangian Systems, J. G. P., Vol. 3, 1986, pp. 353-400. | MR 894631 | Zbl 0621.58020

[11] W. Sarlet, F. Cantrijn and M. Crampin, A New Look at Second Order Equations and Lagrangian Mechanics, J. Phys. A: Math. Gen., Vol. 17, 1984, pp. 1999-2009. | MR 763792 | Zbl 0542.58011

[12] E. Massa and E. Pagani, Classical Dynamics of non-holonomic systems: a geometric approach, Ann. Inst. Henri Poicaré, Vol. 55, 1991, pp. 511-544. | Numdam | MR 1130215 | Zbl 0731.70012

[13] E. Massa and E. Pagani, Jet bundle geometry, dynamical connections, and the inverse problem of Lagrangian Mechanics, Ann. Inst. Henri Poicarré, Vol. 61, 1994, pp. 17-62. | Numdam | MR 1303184 | Zbl 0813.70004

[14] N.G. Chetaev, O printsipe Gaussa (On the Gauss Principle), Izd. Fiz.-Matem. Obshch. pri Kazansk. Univ., Ser. 3, Vol. 6, 1932-1933, pp. 323-326, Izvestia of the Physico-Mathematical Society of Kazan University, Series 3, Vol. 6, 1932-1933, pp. 62-67.

[15] N.G. Chetaev, Papers on Analytical Mechanics. On the Gauss Principles, Moscow, Izd. Akad. Nauk SSSR, 1962.

[16] V.V. Rumiantsev, Certain Variational Principles of Mechanics, in Adv. Theor. Appl. Mech., A. Ishlinsky and F. Chernousko Eds., English translation, MIR Publishers, Moscow, 1981.

[17] I.I. Neimark and N.A. Fufaev, Dynamics of Non-holonomic Systems, Translations of Mathematical Monographs, Vol. 33, American Mathematical Society, Providence, Rhode Island, 1972. | Zbl 0245.70011

[18] Y. Pironneau, Sur les liaisons non holonômes, non linéaires déplacements virtuels à travail nul, conditions de Chetaev, Proceedings of the IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, Academy of Sciences of Turin, Turin, June 7-11, 1982, Atti della Accademia delle Scienze di Torino, Supplemento al Vol. 117, (1983), p. 671-686. | MR 773517

[19] M. De Leon and P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, North Holland, Amsterdam, 1989. | MR 1021489 | Zbl 0687.53001

[20] W. Sarlet, F. Cantrijn and D.J. Saunders, A Geometrical Framework for the Study of Non-holonomic Lagrangian Systems, J. Phys. A.: Math. Gen., Vol. 28, 1995, pp. 3253-3268. | MR 1344117 | Zbl 0858.70013

[21] C. Godbillon, Géométrie Différentielle et Mécanique Analytique, Hermann, Paris, 1969. | MR 242081 | Zbl 0174.24602

[22] R. Abraham and J.E. Marsden, Foundations of Mechanics, The Benjamin/Cumming Publishing Company, Reading (Massachussets), 1978. | MR 515141 | Zbl 0393.70001

[23] R.B. Ash, Measure, Integration and Functional Analysis, Academic Press, New York and London, 1972. | MR 435321 | Zbl 0249.28001

[24] K. Yosida, Functional Analysis, Springer-Verlag, Berlin and New York, 1968. | MR 239384

[25] F. Cardin and G. Zanzotto, On Constrained Mechanical Systems: D'Alembert and Gauss' Principles, J. Math. Phys., Vol. 30, 1989, pp. 1473-1479. | MR 1002251 | Zbl 0678.70018