### Recent Submissions

• #### Multisymplectic unified formalism for Einstein-Hilbert gravity ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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.

(2015-12-30)
Article
Open Access