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David Martín

Institution: Consejo Superior de Investigaciones Científicas

Position: Investigador Científico

Office: 411        Phone:+34 912999 791

E-mail: david.martin()icmat.es

Personal Webpage

 

Biographical Review

David Martin de Diego is a research scientist at the Instituto de Ciencias Matemáticas – ICMAT (Institute of Mathematical Sciences). His work focuses on applications of Geometric mechanics in a wide range of topics such as geometric integrators, nonholonomic mechanics, Hamilton-Jacobi equation, optimal control theory, reduction of lagrangian systems, etc..

His research emphasizes the relationship between differential geometry (symplectic and Poisson geometry, Lie algebroids and groupoids...) and dynamical systems, as for instance, mechanical systems and systems with symmetry even in the area of optimal control.

He has over 90 research papers, including articles in Archives of RationalMechanics and Analysis, Journal of Mathematiques Pures et Apliquees Nonlinearity, SIAM Journal on Control and Optimization, Journal of Nonlinear Science, Discrete and Continuous Dynamical Systems - Series A, Journal of Physics A, etc... See for more details.

Some of his papers have become an outstanding international reference, such as the first derivation of a Hamilton-Jacobi equation for nonholonomic systems, the construction of variational integrators for nonholonomic and reduced mechanical systems and the derivation of a geometric integrator for optimal control of mechanical systems admitting discontinuities in the control variables.

Dr Martín de Diego did his Ph.D. in Mathematics at Universidad Complutense de Madrid in 1995 obtaining the Best Ph.D. Dissertation Award. From 1998-2000 he was an associate professor at the Universidad de Valladolid, Spain. In 2000 he took on his current position at Consejo Superior de Investigaciones Científicas, CSIC.

He is a member of the Editorial Board of the Journal of Geometric Mechanics and he was the Editor-In-Chief of La Gaceta de la Real Sociedad Matemáticas Española (2003-2008). Dr. Martín de Diego is author of two books of popularization of mathematics: Princesas, Abejas y Matemáticas ( see ); Matemáticas del Sistema Solar (coauthored with M. de León and J.C. Marrero, see ).

Publications

Artículos

  1. Ferraro, Sebastián; de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David; Vaquero, Miguel On the geometry of the Hamilton-Jacobi equation and generating functions. Arch. Ration. Mech. Anal. 226 (2017), no. 1, 243–302.
  2. de León, Manuel; de Diego, David Martín; Vaquero, Miguel Hamilton-Jacobi theory, symmetries and coisotropic reduction. J. Math. Pures Appl. (9) 107 (2017), no. 5, 591–614.
  3. Colombo, Leonardo; Ferraro, Sebastián; Martín de Diego, David Geometric integrators for higher-order variational systems and their application to optimal control. J. Nonlinear Sci. 26 (2016), no. 6, 1615–1650.
  4. Colombo, Leonardo; Martín de Diego, David Second-order variational problems on Lie groupoids and optimal control applications. Discrete Contin. Dyn. Syst. 36 (2016), no. 11, 6023–6064.
  5. Barbero-Liñán, María; Farré Puiggalí, Marta; Martín de Diego, David Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries. Monatsh. Math. 180 (2016), no. 4, 665–691.
  6. Colombo, Leonardo; Jiménez, Fernando; Martín de Diego, David Variational integrators for mechanical control systems with symmetries. J. Comput. Dyn. 2 (2015), no. 2, 193–225.
  7. Campos, Cédric M.; de León, Manuel; de Diego, David Martín; Vaquero, Miguel Hamilton-Jacobi theory in Cauchy data space. Rep. Math. Phys. 76 (2015), no. 3, 359–387.
  8. Bloch, Anthony; Colombo, Leonardo; Gupta, Rohit; de Diego, David Martín A geometric approach to the optimal control of nonholonomic mechanical systems. Analysis and geometry in control theory and its applications, 35–64, Springer INdAM Ser., 11, Springer, Cham, 2015.
  9. Marrero, Juan C.; Martín de Diego, David; Martínez, Eduardo The local description of discrete mechanics. Geometry, mechanics, and dynamics, 285–317, Fields Inst. Commun., 73, Springer, New York, 2015.
  10. Ferraro, Sebastián; Jiménez, Fernando; Martín de Diego, David New developments on the geometric nonholonomic integrator. Nonlinearity 28 (2015), no. 4, 871–900.
  11. Barbero-Liñán, María; Iglesias Ponte, David; Martín de Diego, David Morse families in optimal control problems. SIAM J. Control Optim. 53 (2015), no. 1, 414–433.
  12. Barbero-Liñán, María; Farré Puiggalí, Marta; Martín de Diego, David Isotropic submanifolds and the inverse problem for mechanical constrained systems. J. Phys. A 48 (2015), no. 4, 045210, 35 pp.
  13. Marrero, Juan Carlos; Martín de Diego, David; Stern, Ari Symplectic groupoids and discrete constrained Lagrangian mechanics. Discrete Contin. Dyn. Syst. 35 (2015), no. 1, 367–397.
  14. Colombo, Leonardo; Martín de Diego, David; Zuccalli, Marcela On the construction of variational integrators for optimal control of nonholonomic mechanical systems. Proceedings of the XIIth "Dr. Antonio A. R. Monteiro'' Congress, 135–147, Actas Congr. "Dr. Antonio A. R. Monteiro'', Univ. Nac. del Sur, Bahía Blanca, 2014.
  15. Colombo, Leonardo; Martín de Diego, David Higher-order variational problems on Lie groups and optimal control applications. J. Geom. Mech. 6 (2014), no. 4, 451–478.
  16. de León, Manuel; Martín de Diego, David; Vaquero, Miguel A Hamilton-Jacobi theory on Poisson manifolds. J. Geom. Mech. 6 (2014), no. 1, 121–140.
  17. Colombo, Leonardo; Martín de Diego, David Optimal control of underactuated mechanical systems with symmetries. Discrete Contin. Dyn. Syst. 2013, Dynamical systems, differential equations and applications. 9th AIMS Conference. Suppl., 149–158.
  18. Colombo, Leonardo; Martin de Diego, David; Zuccalli, Marcela Higher-order discrete variational problems with constraints. J. Math. Phys. 54 (2013), no. 9, 093507, 17 pp.
  19. Barbero-Liñán, María; de León, Manuel; de Diego, David Martín Lagrangian submanifolds and the Hamilton-Jacobi equation. Monatsh. Math. 171 (2013), no. 3-4, 269–290.
  20. de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David; Vaquero, Miguel On the Hamilton-Jacobi theory for singular Lagrangian systems. J. Math. Phys. 54 (2013), no. 3, 032902, 32 pp.
  21. Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David Discrete variational optimal control. J. Nonlinear Sci. 23 (2013), no. 3, 393–426.
  22. Iglesias-Ponte, David; Marrero, Juan Carlos; Martín de Diego, David; Padrón, Edith Discrete dynamics in implicit form. Discrete Contin. Dyn. Syst. 33 (2013), no. 3, 1117–1135.