Institution: CSIC
Position: Investigador Científico
Office: 411
Phone: +34 912999 791
Email: david.martin@icmat.es
About:
I am Research Scientist at the Instituto de Ciencias Matemáticas-ICMAT, since 2008. My work focuses on the development and study of applications of geometric mechanics in a wide variety of topics, including geometric integration, nonholonomic mechanics, Hamilton-Jacobi theory, optimal control theory, Lagrangian system reduction, robotics and mustily systems, interconnection of mechanical systems, machine learning… My research emphasizes the important relationship between differential geometry (symplectic, Poisson, Dirac structures….) and dynamical systems. (continuous and discrete), such as mechanical systems and systems with symmetries and also in the area of optimal control theory.
I have published about 110 research papers in the main journals of my research area, Foundations of Computational Mathematics, Numerische Mathematik, Archive for Rational Mechanics and Analysis, Journal de Mathématiques Pures et Appliquées, Nonlinearity, SIAM Journal on Control and Optimization, Journal of Nonlinear Science, Discrete and Continuous Dynamical Systems – Series A, Journal of Physics A, etc….
Some of these articles are currently a reference, such as the derivation, for the first time, of the Hamilton-Jacobi equation for nonholonomic systems, the construction of geometric integrators for nonholonomic systems and reduced systems using symplectic groupoids, the derivation of geometric integrators for the optimal control of mechanical systems admitting discontinuities in the control variables or the existence of metrics that minimize the length of the solutions of mechanical nonholonomic systems….
I am member of the Editorial Board of the Journal of Geometric Mechanics and La Gaceta de la RSME of which I was Editor in Chief from 2003-2008. I am also the author of two books on popularization of mathematics: Princesas, Abejas y Matemáticas and Matemáticas y Matemáticas del Sistema Solar (the latter in collaboration with M. de León and J.C. Marrero).
As management positions include the work as Deputy Director of ICMAT (05/02/2016-04/04/2018), Director of the Mathematical Culture Unit of ICMAT since 2007 (scientific culture unit recognized by the FECYT), that of Vice President of the RSME that I have held from 2015 until February 2022 and representative in the Strategic Mathematics Network of ICMAT.
I also highlight the General Coordination of one of the most important works for the Spanish Mathematical community: "El Libro Blanco de las Matemáticas" published by the Ramón Areces Foundation in 2019.
Publications (last five years)
María Barbero Liñán, David Martín de Diego: Retraction maps: a seed of geometric integrators, Accepted in Foundations of Computational Mathematics 2022.
Alexandre Anahory Simoes, Juan Carlos Marrero, David Martin de Diego: Exact discrete Lagrangian mechanics for nonholonomic mechanics, Accepted in Numerische Mathematik 2022.
Anahory Simoes, Alexandre; Martín de Diego, David; Lainz Valcázar, Manuel; de León, Manuel On the geometry of discrete contact mechanics. J. Nonlinear Sci. 31 (2021), no. 3, Paper No. 53, 30 pp.
Anahory Simoes, Alexandre; Marrero, Juan Carlos; Martín de Diego, David Radial kinetic nonholonomic trajectories are Riemannian geodesics! Anal. Math. Phys. 11 (2021), no. 4, Paper No. 152, 28 pp.
Colombo, Leonardo J.; Martín de Diego, David; Nayak, Aradhana; Sato Martín de Almagro, Rodrigo T. Geometric optimal trajectory tracking of nonholonomic mechanical systems. SIAM J. Control Optim. 58 (2020), no. 3, 1652–1675.
Barbero Liñán, M.; Cortés, J.; Martín de Diego, D.; Martínez, S.; Muñoz Lecanda, M. C. Global controllability tests for geometric hybrid control systems. Nonlinear Anal. Hybrid Syst. 38 (2020), 100935, 17 pp.
Elena Celledoni, Elena; Farré Puiggalí, Marta; Hoel Hoiseth Eirik; Martin de Diego, David: Energy-Preserving integrators applied to nonholonomic systems. J. Nonlinear Sci 2019.
Martín de Diego, D.; de Almagro, R. Sato Martín Variational order for forced Lagrangian systems. Nonlinearity 31 (2018), no. 8, 3814–3846.
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.
de León, Manuel; Martín de Diego, David; Vaquero, Miguel Hamilton-Jacobi theory, symmetries and coisotropic reduction. J. Math. Pures Appl. (9) 107 (2017), no. 5, 591–614.
Congress
Noether Symmetries and Decay Laws in Formation Control of Multi-agent Systems. 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Berlin Germany, October 11, 2021
Discrete variational calculus and accelerated methods in optimization, CLAM 2021 Uruguay, September 2021, Invited speaker
Geometric nonholonomic integrators. Conference on the Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-16), 2021.
Geometric integration of mechanical systems and applications to optimal control in the Encontro Nacional da Sociedade Portuguesa de Matemática 2021 (ENSPM2021), held online, between the 12th and 16th of July 2021. Invited speaker.
Variational order for forced Lagrangian discrete dynamics. Fall Central Sectional Meeting. University of Michigan, Ann Arbor, Ann Arbor, MI October 20-21, 2018. Invited speaker.
On the geometry of mechanical systems subject to affine nonholonomic constraints, Dynamics and integrability of nonholonomic and other non-Hamiltonian systems January 24-27, 2018 – Dipartimento di Matematica "Tullio Levi-Civita", Università degli Studi di Padova. Invited speaker.
Workshop on Classic and Stochastic Approaches to Mathematical Fluid Dynamics. 2–6 October 2017, Imperial College, London. Invited speaker.
Variational order for forced Lagrangian systems. Minisimposium Structure-preserving methods for the dynamics and optimal control of structures and multibody systems, ECCM-ECFD 2018, Glasgow, UK. 14 June 2018. Invited speaker.
Research projects (last 10 years)
GEOMETRIC STRUCTURES IN DYNAMICAL SYSTEMS, MECHANICS AND HYDRODYNAMICS , Reference: PID2019-106715GB-C21 Instituto de Ciencias Matemáticas. Principal investigators: David Martín de Diego and Daniel Peralta Salas 2020-2023 Budget 76.287 euros
THE INTERPLAY BETWEEN GEOMETRY, MECHANICS AND CONTROL IN MULTI- AGENT SYSTEMS LINKA20079 Program i-Link+2018. , KTH, Universidad de Groningen, Universidad de California/San Diego Principal investigator: David Martín de Diego, 2019-2020. Budget: 24.000 euros
NEW APPLICATIONS OF GEOMETRIC INTEGRATION IN ENGINEERING EIN2019-103037 Instituto de Ciencias Matemáticas Principal Investigator: David Martín de Diego. Duration: 2019-2021. Budget: 15,500 €.
ANALISIS GEOMETRICO Y NUMERICO DE SISTEMAS DINAMICOS Y APLICACIONES A LA FISICA MATEMATICA, Reference: MTM2016-76072-P, Instituto de Ciencias Matemáticas Principal investigators: David Martín de Diego and Daniel Peralta Salas 2017-2020 Budget: 53.900 euros
ESTRUCTURAS GLOBALES Y METODOS NUMERICOS, SISTEMAS DINAMICOS Y CONTROL CON APLICACIONES EN MECANICA Reference: MTM2010-21186-C02-01 Instituto de Ciencias Matemáticas Principal Investigator: David Martín de Diego 2011-2013 Budget: 122.600 euros
Programme: FP7-PEOPLE-2009-IRSES, Marie Curie International Fellowships Proposal n° 246981 –Acronym: GEOMECH. Name: Geometric Mechanics. Principal investigator (Spain): David Martín de Diego 2012-2014 Budget : 158.400 euros
Doctoral theses supervised in the last ten years
Alexandre Anahory Simoes. Geometric and Numerical aspects of Nonholonomic Mechanics. Directors: Juan Carlos Marrero and David Martín de Diego. Date: November 26, 2021. Institution: Universidad Autónoma de MadridOther information: Predoctoral position at the Centro de Matemática e Aplicações Fundamentais (CMAF), Universidade Lisboa. Currently postdoc at the Centro de Automática y Robótica (CSIC-UPM).
Rodrigo Sato Takuro Martín de Almagro. Discrete Mechanics for Forced and Constrained Systems. Director: David Martín de Diego Date: July 2019. Institution: Universidad Complutense de Madrid. Currently postdoctoral fellow at Friedrich-Alexander-Universität Erlangen Nürnberg, Germany.
Marta Farré-Puiggalí. New developments and applications of the Inverse Problem of the Calculus of Variations. Director: David Martín de Diego. Date: March 21, 2017. Institution: Universidad Complutense de Madrid. Postdoctoral fellow at the University of Michigan, USA until 2020. Senior Postdoc at the University of Antwerp from 2020-2023.
Leonardo Colombo. Geometric and Numerical Methods for Optimal Control of Mechanical Systems, Director: David Martín de Diego. Date: July 3, 2014. Instititution: Universidad Autónoma de Madrid RSME . Vicent Caselles Award. Previous contracts at University of Michigan, KTH Royal Institute of Technology and Juan de la Cierva postdoctoral fellow. Postdoctoral Fellowship of the Junior Leader Fellowship of la Caixa and currently Senior Scientist at the CAR (CSIC-UPM).
Fernando Jiménez. New developments on discrete variational calculus: constrained systems and optimal control Director: David Martín de Diego. Date: June 8, 2012. Institution: University of Zaragoza. Postdoctoral fellow at the Universities of Oxford (UK), Waterloo (Canada), Munich (Germany). Currently at UPM
