Geometric formulation of mechanical systems subjected to time-dependent one-sided constraints

Journal of Physics A: Mathematical and General

Volumn 31, Issue 11, 1998, Pages 2655-2674

  Ibort, Alberto ^a   De León, Manuel ^b   Lacomba, Ernesto A ^c   Marrero, Juan C ^d   De Diego, David Martín ^e   Pitanga, Paulo ^f  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b INSTITUTO DE MATEMÁTICAS Y FÍSICA FUNDAMENTAL   (Spain)

^c DEPARTAMENTO DE QUÍMICA   (Mexico)

^d UNIVERSIDAD DE LA LAGUNA   (Spain)

^e UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA   (Spain)

^f FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039938911     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/11/014     Document Type: Article

References (41)

1. Aimé P 1996 Sur la dynamique des systèmes mécaniques Ann. Inst. Henri Poincaré: Phys. Theor. 64 153-76
2. Albert C 1989 Le théoreme de réduction de Marsden-Weinstein en géometrie cosymplectique et de contact J. Geom. Phys. 6 627-49
3. Aminoff C G, Steane A M, Bouyer P, Desbiolles P, Dalibard J and Cohen-Tannoudji C 1993 Cesium atoms bouncing in a stable gravitational cavity Phys. Rev. Lett. 71 3083-6
4. Appell P 1953 Traité de Mécanique Rationnelle 6th edn, vol 2 (Paris: Gauthier-Villars)
5. Barone F, Grassini R and Mendella G 1997 A generalized Lagrange equation in implicit form for non-conservative mechanics J. Phys. A: Math. Gen. 30 1575-90
6. Bates L and Śniatycki J 1992 Nonholonomic reduction Rep. Math. Phys. 32 99-115
7. Bloch A M, Krishnaprasad P S, Marsden J E and Murray R M 1996 Nonholonomic mechanical systems with symmetry Arch. Rational Mech. Anal. 136 21-99
8. Cantrijn F, de León M, Marrero J C and de Diego D M 1997 Reduction of nonholonomic mechanical systems with symmetries (Proc. Workshop on Non-Holonomic Constraints in Dynamics (Calgary, August 26-29, 1997)) Rep. Math. Phys. to appear
9. Crampin M 1995 Jet bundle techniques in analytical mechanics Quaderm del Consiglio Nationale delle Ricerche, Gruppo Nazionale di Fisica Matematica, n. 47 (Firenze, 1995)
10. Chinea D, de León M and Marrero J C 1994 The constraint algorithm for time-dependent Lagrangians J. Math. Phys. 35 3410-47
11. Fermi E 1945 On the origin of the cosmic radiation Phys. Rev. 75 1169-74
12. Giachetta G 1992 Jet methods in non-holonomic mechanics J. Math. Phys. 33 1652-65
13. Ibort A, Lacomba E A, de León M, de Diego D M and Pitanga P 1997 Mechanical systems subjected to impulsive constraints J. Phys. A: Math. Gen. 30 5835-54
14. Kijowski J and Tulczyjew W M 1979 A Symplectic Framework for Field Theories (Lecture Notes in Physics 107) (Berlin: Springer)
15. Koiller J 1992 Reduction of some classical non-holonomic systems with symmetry Arch. Rational Mech. Anal. 118 113-48
16. Koiller J, Markarian R, Oliffson Kamphorst S and Pinto de Carvalho S 1995 Time-dependent billiards Nonlinearity 8 983-1003
17. Krupková O 1997 Mechanical systems with non-holonomic constraints J. Math. Phys. 38 5098-126
18. Lacomba E A and Tulczyjew W M 1990 Geometric formulation of mechanical systems with one-sided constraints J. Phys. A: Math. Gen. 23 2801-13
19. de León M, Marín J and Marrero J C 1996 The constraint algorithm in the jet formalism Diff. Geom. Applic. 6 275-300
20. de León M and Marrero J C 1993 Constrained time-dependent Lagrangian systems and Lagrangian submanifolds J. Math. Phys. 34 622-44
21. de León M, Marrero J C and de Diego D M 1996 Time-dependent constrained Hamiltonian systems and Dirac brackets J. Phys. A: Math. Gen. 29 6843-59
22. de León M, Marrero J C and de Diego D M 1997 Non-holonomic Lagrangian systems in jet manifolds J. Phys. A: Math. Gen. 30 1167-90
23. de León M, Marrero J C and de Diego D M 1997 Mechanical systems with non-linear constraints Int. J. Theor. Phys. 36 973-89
24. de León M, Marrero J C and de Diego D M 1996 Time-dependent mechanical systems with non-linear constraints Proc. Conf. on Differential Geometry (Budapest July 21-27, 1996)
25. de León M and de Diego D M 1996 On the geometry of non-holonomic Lagrangian systems J. Math. Phys. 37 3389-414
26. de León M and Rodrigues P R 1989 Methods of Differential Geometry in Analytical Mechanics (North-Holland Math. Ser. 152) (Amsterdam: North-Holland)
27. Marie Ch M 1985 Reduction of constrained mechanical systems and stability of relative equilibria Commun. Math. Phys. 174 295-318
28. Marmo G, Mendella G and Tulczyjew W M 1992 Symmetries and constants of the motion for dynamics in implicit form Ann. Inst. H. Poincaré 57 147-66
29. Marmo G, Mendella G and Tulczyjew W M 1995 Integrability of implicit differential equations J. Phys. A: Math. Gen. 28 149-63
30. Neimark J and Fufaev N 1972 Dynamics of Nonholonomic Systems (Translations of Mathematical Monographs 33) (Providence, RI: AMS)
31. Painlevé P 1930 Cours de Mécanique vol 1 (Paris: Gauthier-Villars)
32. Rosenberg R M 1977 Analytical Dynamics of Discrete Systems (New York: Plenum)
33. Ruina A 1997 Non-holonomic stability aspects of piecewise holonomic systems (Proc. Workshop on Non-Holonomic Constraints in Dynamics (Calgary, August 26-29, 1997)) Rep. Math. Phys. to appear
34. Saunders DJ 1989 The Geometry of Jet Bundles (London Math. Soc. Lecture Notes Series 142) (Cambridge: Cambridge University Press)
35. Sarlet W, Cantrijn F and Saunders D J 1995 A geometrical framework for the study of non-holonomic lagrangian systems J. Phys. A: Math. Gen. 28 3253-68
36. Saunders D J, Sarlet W and Cantrijn F 1996 A geometrical framework for the study of non-holonomic lagrangian systems: II J. Phys. A: Math. Gen. 29 4265-74
37. Śniatycki J 1997 Non-holonomic Noether theorem and reduction of symmetries (Proc. Workshop on Non-Holonomic Constraints in Dynamics (Calgary, August 26-29, 1997)) Rep. Math. Phys. to appear
38. Steane A M, Szriftgiser P, Desbiolles P and Dalibard J 1995 Phase modulation of atomic de Broglie waves Phys. Rev. Lett. 74 4972-5
39. Tulczyjew W M 1976 Les sous-variétés lagrangiennes et la dynamique hamiltonienne C.R. Acad. Sci., Paris 283 15-18
40. Tulczyjew W M 1976 Les sous-variétés lagrangiennes et la dynamique lagrangienne C.R. Acad. Sci., Paris 283 675-8
41. Tulczyjew W M 1989 Geometric Formulation of Physical Theories: Statics and Dynamics of Mechanical Systems (Napoli: Bibliopolis)