DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
http://hdl.handle.net/2117/3202
Sun, 24 Jul 2016 16:40:53 GMT2016-07-24T16:40:53ZA Hamiltonian study of the stability and bifurcations for the satellite problem
http://hdl.handle.net/2117/85174
A Hamiltonian study of the stability and bifurcations for the satellite problem
Muñoz Lecanda, Miguel Carlos; Rodríguez Olmos, Miguel Andrés; Teixidó Román, Miguel
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 use the reduced energy-momentum for the stability analysis and the treatment of axisymmetric bodies. We explicitly show the existence of new relative equilibria and study their stability and bifurcation patterns.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00332-015-9257-6
Tue, 05 Apr 2016 09:34:40 GMThttp://hdl.handle.net/2117/851742016-04-05T09:34:40ZMuñoz Lecanda, Miguel CarlosRodríguez Olmos, Miguel AndrésTeixidó Román, MiguelWe 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 use the reduced energy-momentum for the stability analysis and the treatment of axisymmetric bodies. We explicitly show the existence of new relative equilibria and study their stability and bifurcation patterns.Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2
http://hdl.handle.net/2117/85167
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
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.
Tue, 05 Apr 2016 08:00:35 GMThttp://hdl.handle.net/2117/851672016-04-05T08:00:35ZGarcía Naranjo Ortiz de la Huerta, Luis ConstantinoMarrero, Juan CarlosPerez Chavela, ErnestoRodríguez Olmos, Miguel AndrésWe 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.Music and mathematics. From Pythagoras to fractals
http://hdl.handle.net/2117/84848
Music and mathematics. From Pythagoras to fractals
Gràcia Sabaté, Francesc Xavier
Wed, 30 Mar 2016 10:13:59 GMThttp://hdl.handle.net/2117/848482016-03-30T10:13:59ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84706
Matemots
Gràcia Sabaté, Francesc Xavier
Fri, 18 Mar 2016 13:42:33 GMThttp://hdl.handle.net/2117/847062016-03-18T13:42:33ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84705
Matemots
Gràcia Sabaté, Francesc Xavier
Fri, 18 Mar 2016 13:40:51 GMThttp://hdl.handle.net/2117/847052016-03-18T13:40:51ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84704
Matemots
Gràcia Sabaté, Francesc Xavier
Fri, 18 Mar 2016 13:39:23 GMThttp://hdl.handle.net/2117/847042016-03-18T13:39:23ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84703
Matemots
Gràcia Sabaté, Francesc Xavier
Fri, 18 Mar 2016 13:37:28 GMThttp://hdl.handle.net/2117/847032016-03-18T13:37:28ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84702
Matemots
Gràcia Sabaté, Francesc Xavier
Fri, 18 Mar 2016 13:35:16 GMThttp://hdl.handle.net/2117/847022016-03-18T13:35:16ZGràcia Sabaté, Francesc XavierA new multisymplectic unified formalism for second order classical field theories
http://hdl.handle.net/2117/81889
A new multisymplectic unified formalism for second order classical field theories
Prieto Martínez, Pedro Daniel; Román Roy, Narciso
We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified LagrangianHamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincare-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.
Fri, 22 Jan 2016 12:29:06 GMThttp://hdl.handle.net/2117/818892016-01-22T12:29:06ZPrieto Martínez, Pedro DanielRomán Roy, NarcisoWe present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified LagrangianHamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincare-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.Hamilton-Jacobi theory in multisymplectic classical field theories
http://hdl.handle.net/2117/81799
Hamilton-Jacobi theory in multisymplectic classical field theories
de León, Manuel; Prieto Martínez, Pedro Daniel; Román Roy, Narciso; Vilariño, Silvia
The geometric framework for the Hamilton-Jacobi theory developed in [14, 17, 39] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problema is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent
the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
Thu, 21 Jan 2016 11:19:16 GMThttp://hdl.handle.net/2117/817992016-01-21T11:19:16Zde León, ManuelPrieto Martínez, Pedro DanielRomán Roy, NarcisoVilariño, SilviaThe geometric framework for the Hamilton-Jacobi theory developed in [14, 17, 39] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problema is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent
the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.