DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
http://hdl.handle.net/2117/3202
2017-03-25T08:12:03ZVariational principles and symmetries on fibered multisymplectic manifolds
http://hdl.handle.net/2117/101999
Variational principles and symmetries on fibered multisymplectic manifolds
Gaset Rifà, Jordi; Prieto Martínez, Pedro Daniel; Román Roy, Narciso
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 (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.
2017-03-07T08:22:02ZGaset Rifà, JordiPrieto Martínez, Pedro DanielRomán Roy, NarcisoThe 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 (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.The wave equation for stiff strings and piano tuning
http://hdl.handle.net/2117/101752
The wave equation for stiff strings and piano tuning
Gràcia Sabaté, Francesc Xavier; Sanz Perela, Tomás
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. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing on the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.
2017-03-01T06:51:11ZGràcia Sabaté, Francesc XavierSanz Perela, TomásWe 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. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing on the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics
http://hdl.handle.net/2117/100664
Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics
Gaset Rifà, Jordi; Román Roy, Narciso
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 $J^3\pi$. The results are applied to the Hilbert Lagrangian for the Einstein equations. Furthermore, the case of higher-order mechanics is also studied as a particular situation.
2017-02-08T10:31:46ZGaset Rifà, JordiRomán Roy, NarcisoThe 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 $J^3\pi$. The results are applied to the Hilbert Lagrangian for the Einstein equations. Furthermore, the case of higher-order mechanics is also studied as a particular situation.A 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
2016-04-05T09:34:40ZMuñoz 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.
2016-04-05T08:00:35ZGarcía 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
2016-03-30T10:13:59ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84706
Matemots
Gràcia Sabaté, Francesc Xavier
2016-03-18T13:42:33ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84705
Matemots
Gràcia Sabaté, Francesc Xavier
2016-03-18T13:40:51ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84704
Matemots
Gràcia Sabaté, Francesc Xavier
2016-03-18T13:39:23ZGràcia Sabaté, Francesc XavierMatemots
http://hdl.handle.net/2117/84703
Matemots
Gràcia Sabaté, Francesc Xavier
2016-03-18T13:37:28ZGràcia Sabaté, Francesc Xavier