@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}, pages = {1--36}, publisher = {Gauthier-Villars}, volume = {66}, number = {1}, year = {1997}, mrnumber = {1434114}, zbl = {0878.70009}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1997__66_1_1_0/} }
TY - JOUR AU - Massa, Enrico AU - Pagani, Enrico TI - A new look at classical mechanics of constrained systems JO - Annales de l'I.H.P. Physique théorique PY - 1997 SP - 1 EP - 36 VL - 66 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1997__66_1_1_0/ LA - en ID - AIHPA_1997__66_1_1_0 ER -
Massa, Enrico; Pagani, Enrico. A new look at classical mechanics of constrained systems. Annales de l'I.H.P. Physique théorique, Tome 66 (1997) no. 1, pp. 1-36. http://www.numdam.org/item/AIHPA_1997__66_1_1_0/
[1] Mécanique Analytique, (Veuve Desaint, Paris, 1788), in Œuvres de Lagrange, Gauthier-Villars, Paris, 1867-1892.
,[2] Mathematical Methods of Classical Mechanics, MIR, Moscow, 1975.
,[3] Lezioni di Meccanica Razionale, Zanichelli, Bologna, 1984, first edition 1922, second edition 1929.
, ,[4] Uber ein neues allgemeines Grundgesetz der Mechanik, Crelle J. reine Math., Vol. 4, 1829, pp. 232.
,[5] A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, (4th ed.), Cambridge University Press, Cambridge, 1959. | MR | Zbl
,[6] Theoretische Mechanik. Eine einheitliche Einfuhrung in die gesamte Mechanik, Springer-Verlag, Berlin, 1949. | MR | Zbl
,[7] Mechanics, Lectures on Theoretical Physics, Vol. 1, Academic Press, New York, San Francisco, London, 1942. | Zbl
,[8] The Geometry of Jet Bundles, London Mathematical Society, Lecture Note Series 142, Cambridge University Press, 1989. | MR | Zbl
,[9] A Geometrical Version of the Helmholtz Conditions in Time-Dependent Lagrangian Dynamics, J. Phys. A: Math. Gen., Vol. 17, 1984, pp. 1437-1447. | MR | Zbl
, and ,[10] Reduction of Degenerate Lagrangian Systems, J. G. P., Vol. 3, 1986, pp. 353-400. | MR | Zbl
, , and ,[11] A New Look at Second Order Equations and Lagrangian Mechanics, J. Phys. A: Math. Gen., Vol. 17, 1984, pp. 1999-2009. | MR | Zbl
, and ,[12] Classical Dynamics of non-holonomic systems: a geometric approach, Ann. Inst. Henri Poicaré, Vol. 55, 1991, pp. 511-544. | Numdam | MR | Zbl
and ,[13] Jet bundle geometry, dynamical connections, and the inverse problem of Lagrangian Mechanics, Ann. Inst. Henri Poicarré, Vol. 61, 1994, pp. 17-62. | Numdam | MR | Zbl
and ,[14] 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] Papers on Analytical Mechanics. On the Gauss Principles, Moscow, Izd. Akad. Nauk SSSR, 1962.
,[16] Certain Variational Principles of Mechanics, in Adv. Theor. Appl. Mech., A. Ishlinsky and F. Chernousko Eds., English translation, MIR Publishers, Moscow, 1981.
,[17] Dynamics of Non-holonomic Systems, Translations of Mathematical Monographs, Vol. 33, American Mathematical Society, Providence, Rhode Island, 1972. | Zbl
and ,[18] 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
,[19] Methods of Differential Geometry in Analytical Mechanics, North Holland, Amsterdam, 1989. | MR | Zbl
and ,[20] A Geometrical Framework for the Study of Non-holonomic Lagrangian Systems, J. Phys. A.: Math. Gen., Vol. 28, 1995, pp. 3253-3268. | MR | Zbl
, and ,[21] Géométrie Différentielle et Mécanique Analytique, Hermann, Paris, 1969. | MR | Zbl
,[22] Foundations of Mechanics, The Benjamin/Cumming Publishing Company, Reading (Massachussets), 1978. | MR | Zbl
and ,[23] Measure, Integration and Functional Analysis, Academic Press, New York and London, 1972. | MR | Zbl
,[24] Functional Analysis, Springer-Verlag, Berlin and New York, 1968. | MR
,[25] On Constrained Mechanical Systems: D'Alembert and Gauss' Principles, J. Math. Phys., Vol. 30, 1989, pp. 1473-1479. | MR | Zbl
and ,