Silvia Vilari˜no Fernández NUEVAS APORTACIONES AL ESTUDIO ...

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380 Bibliografía [12] I. Bucataru, Linear connections for systems of higher order differential equations, Houston J. Math. 31(2) (2005) 315–332 . [13] A. Cannas da Silva, A. Weinstein, Geometric models for noncommutative algebras, Amer. Math. Soc., Providence, RI, 1999; xiv+184 pp. [14] F. Cantrijn, A. Ibort, M. de León, Hamiltonian structures on multisymplectic manifolds, Rend. Sem. Mat. Univ. Politec. Torino, 54 (1996), 225-236. [15] F. Cantrijn, A. Ibort, M. de León, On the geometry of multisymplectic manifolds, J. Austral. Math. Soc. Ser. A 66 (1999), 303-330. [16] J. F. Cariñena, M. Crampin, L.A. Ibort, On the multisymplectic formalism for first order field theories, J. Geom. Phys.3 (1986), 353400. [17] J.F. Cariñena, C. López, E. Martínez, A new approach to the converse of Noether’s theorem, J. Phys. A: Math. Gen. 22(22) (1989) 4777–4786. [18] M. Castrillón López, P. L. García Pérez, T. S. Ratiu, Euler- Poincaré reduction on principal bundles, Seat. Math. Phys. 58 (2001), no. 2, 167-180. [19] M. Castrillón López, T. S. Ratiu, Reduction in principal bundles: covariant Lagrange-Poincaré equations, Comm. Math. Phys. 236 (2003), no. 2, 223–250. [20] M. Castrillón López, J.E. Marsden, Covariant and dynamical reduction for principal bundle field theories, Ann Dlob Anal Geom (2008), 34, 263-285. [21] H. Cendra, J. E. Marsden, T.S. Ratiu: Lagrangian reduction by stages, Mem. Amer. Soc. 152 (722) 2001. [22] J. Cortés, Geometric, control and numerical aspects of nonholonomic systems, Lecture Notes in Mathematics, vol. 1793, Springer-Verlag, Berlin, 2002. [23] J. Cortés, M. de León, D. Martín de Diego, S. Martínez, Geometric description of vakonomic and nonholonomic dynamics. Comparison of soluciones, SIAM J. Control Optim. 41 (2002) 1389-1412. [24] J. Cortés, M. De León, J.C. Marrero, D. Martín de Diego, E. Martinez, A survey of. Lagrangian mechanics and control on Lie algebroids and groupoids. Int. J. Geom. Methods Mod. Phys. 3 (2006), no. 3, 509–558.
Bibliografía 381 [25] J. Cortés, S. Martínez, F. Cantrijn, Skinner-Rusk approach to timedependent mechanics, Phys. Seat. A 300 (2002) 250-258. [26] M. Crampin, On horizontal distributions on the tangent bundle of a differentiable manifold, J. London Math. Soc. (2) 3 (1971) 178-182. [27] M. Crampin, Defining Euler-Lagrange fields in terms of almost tangent structures, Phys. Lett. A 95 (1983) 466-468. [28] M. Crampin, Generalized Bianchi identities for horizontal distributions, Math. Proc. Camb. Phil. Soc. 94 (1983) 125-132. [29] M. Crampin, Connections of Berwald type, Publ. Math. Debrecen 57 (2000) 455-473. [30] M. Crampin, Tangent bundle geometry for Lagrangian dynamics, J. Phys. A: Math. Gen. 16 (1983), 3755–3772. [31] E. Durand : Électrostatique, les distributions, Mason et Cie Editeurs, Paris 1964. [32] A. Echeverría-Enríquez, C. López, J. Marín-Solano, M.C. Muñoz- Lecanda, N. Román-Roy, Lagrangian-Hamiltonian unified formalism for field theory. J. Math. Phys. 45(1) (2004) 360-380. [33] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy, Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries, J. Phys. A: Math. Gen. 32(48) (1999) 8461-8484. [34] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy, Non-standard connections in classical mechanics. J. Phys. A: Math. Gen. 28(19) (1995) 5553-5567. [35] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy, Geometry of Lagrangian first-order classical field theories. Fortsch. Phys. 44(3) (1996) 235-280. [36] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy, Geometry of Multisymplectic Hamiltonian First-order Field Theories. J. Math. Phys. 41(11) (2000) 7402-7444. [37] A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy, Geometrical setting of time-dependent regular systems: Alternative models. Rev. Math. Phys. 3(3) (1991) 301-330.
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Silvia Vilariño Fernández NUEVAS
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A mi familia
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Índice general Agradecimientos VII
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4.1. La sucesión exacta corta cons
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7.2.1. Estructura k-cosimpléctica.
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y k-cosimpléctico, de modo que los
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Capítulo 6: Formulación k-cosimpl
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Capítulo 1 Formulación k-simpléc
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1.1.1 Fundamentos geométricos. 5 E
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1.1.1 Fundamentos geométricos. 7 (
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1.1.1 Fundamentos geométricos. 9 D
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1.1.2 Campos de k-vectores y seccio
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1.1.3 Formalismo hamiltoniano. Ecua
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1.2 El enfoque lagrangiano. 21 Teni
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1.2.1 Elementos geométricos. 23 El
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1.2.1 Elementos geométricos. 25 Ob
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1.2.1 Elementos geométricos. 27 De
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1.2.3 Campos de k-vectores y sopde
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1.2.3 Campos de k-vectores y sopde
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1.2.4 Formalismo lagrangiano. Ecuac
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1.3 Equivalencia entre las formulac
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44 2 Simetrías y Leyes de conserva
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Capítulo 3 Teoría de Campos con l
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3.1.2 El fibrado de las formas de l
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3.1.4 Las ecuaciones de campo no-ho
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3.2 El proyector no-holonómico. 87
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3.2 El proyector no-holonómico. 89
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3.3 La ecuación momento no-holonó
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3.4.1 “Cosserat rods”(Barra Cos
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3.4.1 “Cosserat rods”(Barra Cos
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3.4.3 Ligaduras lineales. 101 Si la
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3.4.3 Ligaduras lineales. 103 donde
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3.4.3 Ligaduras lineales. 105 Demos
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3.4.4 Ligaduras definidas por conex
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3.5 Teoría hamiltoniana k-simpléc
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3.5 Teoría hamiltoniana k-simpléc
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114 4 Relación entre conexiones no
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144 5 Formulación k-simpléctica e
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Capítulo 6 Formulación k-cosimpl
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6.1.1 Fundamentos geométricos. 225
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6.2.1 Elementos geométricos. 241 f
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6.2.1 Elementos geométricos. 243 p
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6.2.1 Elementos geométricos. 245 d
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6.2.2 Ecuaciones en derivadas parci
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6.2.2 Ecuaciones en derivadas parci
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6.2.3 Formalismo lagrangiano: ecuac
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6.3 Equivalencia entre la formulaci
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266 7 Formalismo k-cosimpléctico y
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308 8 Formalismo k-cosimpléctico e
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Page 389 and 390: Apéndice C Índice de símbolos En
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Page 395 and 396: Conclusiones. El punto de partida d
Page 397: Bibliografía [1] R. Abraham-J. E.
Page 401 and 402: Bibliografía 383 [50] M.J. Gotay,
Page 403 and 404: Bibliografía 385 [75] M. de León,
Page 405 and 406: Bibliografía 387 [100] E. Martíne
Page 407 and 408: Bibliografía 389 [124] D. J. Saund
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Silvia Vilari˜no Fernández NUEVAS APORTACIONES AL ESTUDIO ...

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