Ara es mostren els items 1-20 de 20

  • 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
    Accés obert
    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 ...
  • Constraint algorithm for extremals in optimal control problems 

    Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos (2007-07-27)
    Article
    Accés obert
    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 ...
  • Geometric approach to Pontryagin's Maximum Principle 

    Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos (Springer Netherlands, 2008-10)
    Article
    Accés obert
    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 

    Cariñena, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2006-04-21)
    Article
    Accés obert
    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 ...
  • 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)
    Report de recerca
    Accés obert
    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 ...
  • Hamiltonian Systems in Multisymplectic Field Theories 

    Echeverría Enríquez, Arturo; León, Manuel de; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2005-06-20)
    Article
    Accés obert
    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 ...
  • 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)
    Capítol de llibre
    Accés obert
    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)
    Capítol de llibre
    Accés obert
    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 ...
  • Hilbert, un matemático para la eternidad 

    Muñoz Lecanda, Miguel Carlos (2017-09-27)
    Audiovisual
    Accés obert
    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 ...
  • Kinematic reduction and the Hamilton-Jacobi equation 

    Barbero Liñán, María; De León, Manuel; Martin de Diego, David; Marrero, Juan Carlos; Muñoz Lecanda, Miguel Carlos (American Institute of Mathematical Sciences, 2012)
    Article
    Accés obert
    A close relationship between the classical Hamilton- Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship ...
  • Maryam Mirzakhani, una llum que mai no s’apagarà 

    Miranda Galcerán, Eva; Muñoz Lecanda, Miguel Carlos (Societat Catalana de Matemàtiques (SCM), 2017-12-31)
    Article
    Accés obert
  • On some aspects of the geometry of non integrable distributions and applications 

    Muñoz Lecanda, Miguel Carlos (American Institute of Mathematical Sciences, 2018-12-01)
    Article
    Accés obert
    We consider a regular distribution D in a Riemannian manifold (M, g). The LeviCivita connection on (M, g) together with the orthogonal projection allow to endow the space of sections of D with a natural covariant derivative, ...
  • Optimal control problems for affine connection control systems: characterization of extremals 

    Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos (American Institute of Physics, 2008-02)
    Text en actes de congrés
    Accés obert
    Pontryagin’s Maximum Principle [8] is considered as an outstanding achievement of optimal control theory. This Principle does not give sufficient conditions to compute an optimal trajectory; it only provides necessary ...
  • Origen y desarrollo histórico del cálculo infinitesimal 

    Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (Edicions UPC, 1999)
    Llibre
    Accés restringit a la comunitat UPC
    Esta obra intenta dar una visión de la evolución histórica del cálculo infinitesimal: Los problemas originales en el siglo XVII, la aportación realizada por Newton y Leibnitz que consistió fundamentalmente en efectuar una ...
  • Skinner-Rusk formalism for optimal control 

    Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2006-12)
    Article
    Accés obert
    In 1983, the dynamics of a mechanical system was represented by a first-order system on a suitable phase space by R. Skinner and R. Rusk. The corresponding unified formalism developed for optimal control systems allows us ...
  • Skinner-Rusk unified formalism for optimal control systems and applications 

    Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2007-05-15)
    Article
    Accés obert
    A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed ...
  • Strict abnormal extremals in nonholonomic and kinematic control systems 

    Barbero Liñán, María; Muñoz Lecanda, Miguel Carlos (2008-06)
    Article
    Accés obert
    In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals ...
  • Structural aspects of Hamilton–Jacobi theory 

    Cariñena Marzo, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez Fernandez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2016-02-01)
    Article
    Accés obert
    In our previous papers [11, 13] we showed that the Hamilton–Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. ...
  • Unified formalism for non-autonomous mechanical systems 

    Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (AIP, 2008-06-01)
    Working paper
    Accés obert
    We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). ...
  • Unified formalism for non-autonomous mechanical systems 

    Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (2008-02-29)
    Article
    Accés obert
    We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk ...