Recent Papers

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In production

• Geometric Hamilton-Jacobi theory
  José F. Cariñena, Xavier Gràcia, Giuseppe Marmo, Eduardo Martínez, Miguel C. Muñoz-Lecanda and Narciso Román-Roy
  preprint
• Variational Calculus on Lie Algebroids
  Eduardo Martínez
  preprint
• A new geometrical setting for the Hamilton-Jacobi equation
  José F. Cariñena, Xavier Gràcia, Giuseppe Marmo, Eduardo Martínez, Miguel C. Muñoz-Lecanda and Narciso Román-Roy
  Procs. of the XIV Fall Workshop on Geometry and Physics, Bilbao (Spain), 2004. Publicaciones de la RSME. (to appear)
• On second Noether's theorem and gauge symmetries in mechanics
  José F. Cariñena, Joan-Andreu Lázaro-Camí and Eduardo Martínez
  To appear in International Journal on Geometric Methods in Mathematical Physics
• A survey of Lagrangian mechanics and control on Lie algebroids and groupoids
  Jorge Cortes, Manuel de Leon, Juan Carlos Marrero, David Martín de Diego and Eduardo Martínez
  To appear in International Journal on Geometric Methods in Mathematical Physics
• Non-holonomic Lagrangian systems on Lie algebroids
  Jorge Cortés, Manuel de León, Juan Carlos Marrero and Eduardo Martínez
  Submitted
• Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
  Juan Carlos Marrero, David Martín de Diego and Eduardo Martínez
  Submitted
• Classical Field theory on Lie algebroids: multisymplectic formalism
  Eduardo Martínez
  Submitted
• Hamiltonian Mechanics on Lie algebroids
  Eduardo Martínez
  Preprint

Published

• Classical Field theory on Lie algebroids: Variational aspects
  Eduardo Martínez
  Journal of Physics A.: Math. Gen. 38 (2005) 7141-7160
• Lagrangian submanifolds and dynamics on Lie algebroids
  Manuel de León, Juan Carlos Marrero and Eduardo Martínez
  Journal of Physics A.: Math. Gen. (Topical Review) 38 (2005) R241-R308
• Controlability of mechanical control systems on Lie algebroids
  Jorge Cortés and Eduardo Martínez
  IMA Journal of Mathematical Control and Information 21 (2004) 457-492
• Parallel transport and decoupling
  Eduardo Martínez
  In Applied Differential Geometry and Mechanics (In honour of the 60th birthday of Michael Crampin) 2002, Willy Sarlet and Frans Cantrijn Editors.
• Reduction in optimal control theory
  Eduardo Martínez
  Reports on Mathematical Physics 53 (2004) 79-90
• Note on generalised connections and affine bundles
  Tom Mestdag, Willy Sarlet and Eduardo Martínez
  Journal of Physics A: Mat. Gen. 35 (2002) 9843-9865
• Lie Algebroid structures and Lagrangian systems on affine bundles
  Eduardo Martínez, Tom Mestdag and Willy Sarlet
  Journal of Geometry and Physics 44 (2002) 70-95
• Lie Algebroids: some generalizations and applications
  Eduardo Martínez
  Procs. of the XI Fall Workshop on Geometry and Physics, Oviedo(Spain), 2002. Publicaciones de la RSME
• Lie Algebroid structures on a class of affine bundles
  Willy Sarlet, Tom Mestdag and Eduardo Martínez
  Journal of Mathematical Physics 43 (2002) 5654-5674
• Lagrangian equations on affine Lie algebroids
  Willy Sarlet, Tom Mestdag and Eduardo Martínez
  In Differential Geometry and its Applications Matemathical Publications of Silesian university at Opava, 2003. Procs. of the 8th Conference on Differential Geometry and its Applications, Opava (Check republic), 2001. O. Kowalski, D. Krupka and J. Slovák, Editors
• Lie Algebroid generalization of Geometric Mechanics
  José F. Cariñena and Eduardo Martínez
  In Lie Algebroids and related topics in differential geometry (Warsaw 2000). Banach Center Publications 54 2001, p. 201
• Symmetries, Symplectic Formalism and Super-Integrability
  Carlos López, Eduardo Martínez and Manuel Fernández-Rañada
  Procs. of the IX Fall Workshop on Geometry and Physics, Vilanova y La Geltrú (Spain), 2000. X. Gràcia, J. Marín-Solano, M. C. Muñoz-Lecanda and N. Román-Roy, editors. Publicaciones de la RSME, 2001
• Lagrangian Mechanics on Lie algebroids
  Eduardo Martínez
  Acta Applicandae Mathematicae 67 (2001) 295-320
• Sub-Finslerian metric associated to an Optimal Control system
  Carlos López and Eduardo Martínez
  SIAM J. Control and Optim. 39 3 (2000) 798-811
• Generalized metric on optimal control systems
  Carlos López and Eduardo Martínez
  Procs. del VII Encuentro de Otoño de Geometría y Física, Valencia (Spain), 1998. Elisa Llinares y Juán Monterde editors. Publicaciones de la RSME, 1999
• Dynamical symmetries, Non-Cartan symmetries, and superintegrability of the n-dimensional harmonic oscillator
  Manuel Fernández-Rañada, Carlos López and Eduardo Martínez
  J. Phys. A: Math. Gen. 32(1999) 1241-1249
• Geometric Formulation of Mechanics on Lie algebroids
  Eduardo Martínez
  Procs. of the IX Fall Workshop on Differential Geometry and its Applications (Medina del Campo, SPAIN) 1999, M. Del Olmo and M.Santander Eds.
• The integrability conditions in the inverse problem of the calculus of variations for second-order differential equations
  Willy Sarlet, Mike Crampin and Eduardo Martínez
  Acta Applicandae Mathematicae 54 (1998) 233-273
• Linear connection for systems of second-order ordinary differential equations
  Mike Crampin, Eduardo Martínez and Willy Sarlet
  Ann. Inst. H. Poincaré 65 (1996) 223-249
• Complete separability of systems of time-dependent second-order differential equations
  Frans Cantrijn, Willy Sarlet, Ann Vandecasteele and Eduardo Martínez
  Acta Applicandae Mathematicae 42 (1996) 309-334
• Derivations of forms along a map: the framework for time-dependent second-order equations
  Willy Sarlet, Ann Vandecasteele, Frans Cantrijn and Eduardo Martínez
  Differential Geometry and its Applications 5 (1995) 171-203
• Geometric characterization of linearizable second-order differential equations
  Eduardo Martínez and José F. Cariñena
  Math. Procs. Camb. Phil. Soc. 119 (1996) 373-381
• Application of the theory of separability of second-order differential equations
  Willy Sarlet, Frans Cantrijn and Eduardo Martínez
  Nonlinear Mathematical Physics 1 (1994) 5-24
• Towards a geometrical understanding of Douglas's solution of the inverse problem of the calculus of variations
  Mike Crampin, Willy Sarlet, Eduardo Martínez, Graham Byrnes and Geoff Prince
  Inverse Problems 10 (1994) 245-260
• A new geometric setting for Lax equations
  Eduardo Martínez and José F. Cariñena
  Int. Jour. Mod. Phys. 9 (28) (1994) 321-334
• Geometric characterization of separable second-order differential equations
  Eduardo Martínez, José F. Cariñena and Willy Sarlet
  Math. Procs. Camb. Phil. Soc. 113 (1993) 205-224
• Derivations of differential forms along the tangent bundle projection. Part II
  Eduardo Martínez, José F. Cariñena and Willy Sarlet
  Differential Geometry and its Applications 3 (1993) 1-29
• Noether's Theorem in time-dependent Lagrangian Mechanics
  José F. Cariñena, José Fernández-Núñez and Eduardo Martínez
  Reports in Mathamatical Physics 31 (1992) 189-203
• Derivations of differential forms along the tangent bundle projection
  Eduardo Martínez, José F. Cariñena and Willy Sarlet
  Differential Geometry and its Applications 2 (1992) 17-43
• A geometric approach to the Second Noether's Theorem in time-dependent Lagrangian Mechanics
  José F. Cariñena, José Fernández-Núñez and Eduardo Martínez
  Letters in Mathematical Physics 23 (1991) 51-63
• Sections along a map applied to higher-order Mechanics. Noether's Theorem
  José F. Cariñena, Carlos López and Eduardo Martínez
  Acta Applicandae Mathematicae 25 (1991) 127-151
• A new approach to the converse of Noether's theorem
  José F. Cariñena, Carlos López and Eduardo Martínez
  J. Phys A: Math. Gen. 22 (1989) 4777-4786
• A geometric characterization of Lagrangian second-order differential equations
  José F. Cariñena, Carlos López and Eduardo Martínez
  Inverse Problems 5 (1989) 691-705
• Symmetry theory and Lagrangian Inverse Problem for time-dependent second order differential equations
  José F. Cariñena and Eduardo Martínez
  J. Phys. A: Math. Gen. 22 (1989) 2659-2665
• Geometría de ecuaciones diferenciales aplicada a la Mecánica
  Eduardo Martínez
  Ph. D. Thesis. Publicaciones del Seminario Garcia Galdeano. (Only in Spanish)