Now showing items 1-20 of 33

    • A contact geometry framework for field theories with dissipation 

      Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso (2020-03-01)
      Article
      Open Access
      We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of k-contact structure and k-contact Hamiltonian system. This is a generalization ...
    • A Hamiltonian study of the stability and bifurcations for the satellite problem 

      Muñoz Lecanda, Miguel Carlos; Rodríguez Olmos, Miguel Andrés; Teixidó Román, Miguel (2015-10-01)
      Article
      Open Access
      We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometric framework of Wang et al. Novelties of our work are the ...
    • A K-contact Lagrangian formulation for nonconservative field theories 

      Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso (2021-06-01)
      Article
      Restricted access - publisher's policy
      Dynamical systems with dissipative behaviour can be described in terms of contact manifolds and a modified version of Hamilton's equations. Dissipation terms can also be added to field equations, as showed in a recent paper ...
    • ¿Cambia la noción de "pi" si cambia el ambiente? 

      Muñoz Lecanda, Miguel Carlos (Real Sociedad Matemática Española, 2019-03-14)
      Article
      Open Access
      Partiendo de las ideas clásicas sobre la definición de p en el plano geométrico, se extienden esas ideas al caso de superficies de revolución y también a dimensiones superiores a dos. En este último caso se proponen y ...
    • CÀLCUL DIFERENCIAL 

      Muñoz Lecanda, Miguel Carlos (Universitat Politècnica de Catalunya, 2012-07-03)
      Exam
      Restricted access to the UPC academic community
    • CÀLCUL DIFERENCIAL 

      Muñoz Lecanda, Miguel Carlos (Universitat Politècnica de Catalunya, 2012-06-08)
      Exam
      Restricted access to the UPC academic community
    • Cálcul II (Examen 2n quadrimestre) 

      Muñoz Lecanda, Miguel Carlos (Universitat Politècnica de Catalunya, 2007-05-24)
      Exam
      Restricted access to the UPC academic community
    • Cálcul II (Examen 2n quadrimestre) 

      Muñoz Lecanda, Miguel Carlos (Universitat Politècnica de Catalunya, 2007-07-03)
      Exam
      Restricted access to the UPC academic community
    • Constrained Lagrangian dissipative contact dynamics 

      de León Rodríguez, Manuel; Lainz Valcázar, Manuel; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2021-12-28)
      Article
      Restricted access - publisher's policy
      We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate ...
    • Constraint algorithm for extremals in optimal control problems 

      Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos (2007-07-27)
      Article
      Open Access
      A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of ...
    • Fonaments de la matemàtica. Resums, exercicis i problemes 

      Martí Farré, Jaume; Mora Giné, Mercè; Muñoz Lecanda, Miguel Carlos (Universitat Politècnica de Catalunya, 2014)
      Problem statement, exercise
      Open Access
    • Geometric approach to Pontryagin's Maximum Principle 

      Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos (Springer Netherlands, 2008-10)
      Article
      Open Access
      Since the second half of the 20th century, Pontryagin’s Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we ...
    • Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems 

      Cariñena, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2009-08-14)
      Research report
      Open Access
      The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi ...
    • Geometric Hamilton–Jacobi Theory 

      Cariñena, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2006-04-21)
      Article
      Open Access
      The Hamilton–Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias ...
    • Global controllability tests for geometric hybrid control systems 

      Barberó Liñan, María; Cortés, Jorge; Martín de Diego, David; Martínez, Sonia; Muñoz Lecanda, Miguel Carlos (2020-11-01)
      Article
      Restricted access - publisher's policy
      This paper introduces a novel geometric framework to define and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain ...
    • Hamilton-Jacobi theory and the evolution operator 

      Cariñena, José F.; Gràcia Sabaté, Francesc Xavier; Martínez, Eduardo; Marmo, Giuseppe; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (Prensas Univ. Zaragoza, 2009-04)
      Part of book or chapter of book
      Open Access
      We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in ...
    • Hamilton-Jacobi theory and the evolution operator 

      Cariñena Marzo, José Fernando; Gràcia Sabaté, Francesc Xavier; Martínez Fernández, Eduardo; Marmo, Giuseppe; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (Universidad de Zaragoza, Prensas Universitarias de Zaragoza, 2009)
      Part of book or chapter of book
      Open Access
      We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in ...
    • Hamiltonian Systems in Multisymplectic Field Theories 

      Echeverría Enríquez, Arturo; León, Manuel de; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2005-06-20)
      Article
      Open Access
      We consider Hamiltonian systems in first-order multisymplectic field theories. First we review the construction and properties of Hamiltonian systems in the so-called restricted multimomentum bundle using Hamiltonian ...
    • Higher-order contact mechanics 

      De León, Manuel; Gaset Rifà, Jordi; Lainz Valcázar, Manuel; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (Elsevier, 2021-02-01)
      Article
      Restricted access - publisher's policy
      We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent ...
    • Hilbert, un matemático para la eternidad 

      Muñoz Lecanda, Miguel Carlos (2017-09-27)
      Audiovisual
      Open Access
      La FME dedica este curso 2017-18 al matemático David Hilbert, 1862-1943. En esta exposición inicial se comienza presentando su vida, tanto personal como académica, así como aquellos rasgos de su personalidad humana que le ...