Free access
Issue
ESAIM: COCV
Volume 14, Number 2, April-June 2008
Page(s) 356 - 380
DOI http://dx.doi.org/10.1051/cocv:2007056
Published online 20 March 2008
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  2. C. Altafini Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric ESAIM: COCV 10 (2004) 526–548
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  4. A. Cannas da Silva and A. Weinstein Geometric models for noncommutative algebras Amer. Math. Soc., Providence, RI (1999) xiv + 184 pp
  5. J.F. Cariñena and E. Martínez Lie algebroid generalization of geometric mechanics in Lie Algebroids and related topics in differential geometry (Warsaw 2000), Banach Center Publications 54 (2001) 201
  6. H. Cendra, A. Ibort and J.E. Marsden Variational principal fiber bundles: a geometric theory of Clebsch potentials and Lin constraints J. Geom. Phys 4 (1987) 183–206
  7. H. Cendra, J.E. Marsden and T.S. Ratiu Lagrangian reduction by stages Mem. Amer. Math. Soc 152 (2001) x + 108 pp
  8. H. Cendra, J.E. Marsden, S. Pekarsky and T.S. Ratiu Variational principles for Lie-Poisson and Hamilton-Poincaré equations Moscow Math. J 3 (2003) 833–867
  9. J. Cortés, M. de León, J.C. Marrero and E. Martínez Nonholonomic Lagrangian systems on Lie algebroids Preprint 2005, arXiv:math-ph/0512003
  10. J. Cortés, M. de León, J.C. Marrero, D. Martín de Diego and E. Martínez A survey of Lagrangian mechanics and control on Lie algebroids and groupoids Int. J. Geom. Meth. Math. Phys 3 (2006) 509–558
  11. M. Crainic and R.L. Fernandes Integrability of Lie brackets Ann. Math 157 (2003) 575–620
  12. M. Crampin Tangent bundle geometry for Lagrangian dynamics J. Phys. A: Math. Gen 16 (1983) 3755–3772
  13. M. de León, J.C. Marrero and E. Martínez Lagrangian submanifolds and dynamics on Lie algebroids J. Phys. A: Math. Gen 38 (2005) R241–R308
  14. K. Grabowska, J. Grabowski and P. Urbanski Geometrical Mechanics on algebroids Int. Jour. Geom. Meth. Math. Phys 3 (2006) 559–576
  15. D.D. Holm, J.E. Marsden and T.S. Ratiu The Euler-Poincaré equations and semidirect products with applications to continuum theories Adv. Math 137 (1998) 1–81
  16. J. Klein Espaces variationnels et mécanique Ann. Inst. Fourier 12 (1962) 1–124
  17. S. Lang Differential manifolds Springer-Verlag, New-York (1972)
  18. C. López Variational calculus, symmetries and reduction Int. J. Geom. Meth. Math. Phys 3 (2006) 577–590
  19. K.C.H. Mackenzie General Theory of Lie Groupoids and Lie Algebroids Cambridge University Press (2005)
  20. J.E. Marsden and T.S. Ratiu Introduction to Mechanics and symmetry Springer-Verlag, 1999
  21. E. Martínez Lagrangian Mechanics on Lie algebroids Acta Appl. Math 67 (2001) 295–320
  22. E. Martínez Geometric formulation of Mechanics on Lie algebroids, in Proceedings of the VIII Fall Workshop on Geometry and Physics, Medina del Campo, 1999, Publicaciones de la RSME 2 (2001) 209–222
  23. E. Martínez Reduction in optimal control theory Rep. Math. Phys 53 (2004) 79–90
  24. E. Martínez Classical field theory on Lie algebroids: Multisymplectic formalism Preprint 2004, arXiv:math.DG/0411352
  25. E. Martínez Classical Field Theory on Lie algebroids: Variational aspects J. Phys. A: Mat. Gen 38 (2005) 7145–7160
  26. E. Martínez, T. Mestdag and W. Sarlet Lie algebroid structures and Lagrangian systems on affine bundles J. Geom. Phys 44 (2002) 70–95
  27. P. Michor Topics in differential geometry Book on the internet. http://www.mat.univie.ac.at/~michor/dgbook.pdf
  28. J.P. Ortega and T.S. Ratiu Momentum maps and Hamiltonian Reduction Birkhäuser (2004)
  29. P. Piccione and D. Tausk Lagrangian and Hamiltonian formalism for constrained variational problems Proc. Roy. Soc.Edinburgh Sect. A 132 (2002) 1417–1437
  30. W. Sarlet, T. Mestdag and E. Martínez Lagrangian equations on affine Lie algebroids Differential Geometry and its Applications, in Proc. 8th Int. Conf. (Opava 2001), D. Krupka et al Eds
  31. A. Weinstein Lagrangian Mechanics and groupoids Fields Inst. Comm 7 (1996) 207–231