DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions

 

Our main research topic is applied differential geometry. In particular
geometric structures in physics: lagrangian and hamiltonian formalisms, high-order systems, time-dependent systems, classical field theory, singular differential equations, symmetries and reduction, hamilton-jacobi theory, geometric quantization. And geometric methods in control theory: control of mechanical systems, geometric and algebraic control, optimal control and singular systems.

http://futur.upc.edu/DGDSA

Recent Submissions

  • Continuous singularities in hamiltonian relative equilibria with abelian momentum isotropy 

    Rodríguez Olmos, Miguel Andrés (American Institute of Mathematical Sciences, 2020)
    Article
    Restricted access - publisher's policy
    We survey several aspects of the qualitative dynamics around Hamiltonian relative equilibria. We pay special attention to the role of continuous singularities and its effect in their stability, persistence and bifurcations. ...

  • Multisymplectic unified formalism for Einstein-Hilbert gravity 

    Gaset Rifà, Jordi; Román Roy, Narciso (2018-03-01)
    Article
    Open Access
    We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of ...

  • Hamilton-Jacobi theory in multisymplectic classical field theories 

    De León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño Fernández, Silvia (2017-09-01)
    Article
    Open Access
    The geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 ...

  • The Hamiltonian tube of a cotangent-lifted action 

    Rodríguez Olmos, Miguel Andrés; Teixidó Román, Miguel (2017)
    Article
    Open Access
    The Marle-Guillemin-Sternberg (MGS) form is local model for a neighborhood of an orbit of a Hamiltonian Lie group action on a symplectic manifold. One of the main features of the MGS form is that it puts simultaneously in ...

  • Regularity properties of fiber derivatives associated with higher-order mechanical systems 

    Colombo, Leonardo; Prieto Martínez, Pedro Daniel (2016-08)
    Article
    Open Access
    The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More precisely, given a function in T*T(k-1)Q, ...

  • Equivalence between the Hamiltonian and Lagrangian formalisms for constrained systems 

    Batlle Arnau, Carles; Gomis Torné, Joaquin; Pons Ràfols, Josep Maria; Román Roy, Narciso (1986-08)
    Article
    Open Access
    The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints ...

  • 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
    Open Access
    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. ...

  • Variational principles and symmetries on fibered multisymplectic manifolds 

    Gaset Rifà, Jordi; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2016-12-01)
    Article
    Open Access
    The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities ...

  • The wave equation for stiff strings and piano tuning 

    Gràcia Sabaté, Francesc Xavier; Sanz Perela, Tomás (2017)
    Article
    Open Access
    We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. ...

  • Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics 

    Gaset Rifà, Jordi; Román Roy, Narciso (2016-12-01)
    Article
    Open Access
    The consequences of the projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ to a lower-order jet bundle are analyzed using the constraint algorithm for the Euler-Lagrange equations in $J^3\pi$. ...

  • 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 ...

  • Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2 

    García Naranjo Ortiz de la Huerta, Luis Constantino; Marrero, Juan Carlos; Perez Chavela, Ernesto; Rodríguez Olmos, Miguel Andrés (2016-01-13)
    Article
    Open Access
    We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem.

View more