Zobrazeno 1 - 10
of 108
pro vyhledávání: '"de Diego, David Martin"'
In this paper, we prove that the trajectories of unreduced $\phi$-simple Chaplygin kinetic systems are reparametrizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannia
Externí odkaz:
http://arxiv.org/abs/2409.18648
While the construction of symplectic integrators for Hamiltonian dynamics is well understood, an analogous general theory for Poisson integrators is still lacking. The main challenge lies in overcoming the singular and non-linear geometric behavior o
Externí odkaz:
http://arxiv.org/abs/2409.04342
Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well know examples of momentum-descent methods for optimization. While the latter outperforms the former, solely general
Externí odkaz:
http://arxiv.org/abs/2404.09363
This paper presents a general method to construct Poisson integrators, i.e., integrators that preserve the underlying Poisson geometry. We assume the Poisson manifold is integrable, meaning there is a known local symplectic groupoid for which the Poi
Externí odkaz:
http://arxiv.org/abs/2403.20139
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as well as the
Externí odkaz:
http://arxiv.org/abs/2401.14800
In this paper we will study some interesting properties of modifications of the Euler-Poincar\'e equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism. The metripl
Externí odkaz:
http://arxiv.org/abs/2401.05220
This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system respecting i
Externí odkaz:
http://arxiv.org/abs/2308.16331
Autor:
Simoes, Alexandre Anahory, Colombo, Leonardo, de León, Manuel, Marrero, Juan Carlos, de Diego, David Martín, Padrón, Edith
We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain E
Externí odkaz:
http://arxiv.org/abs/2306.07028
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the discretization ru
Externí odkaz:
http://arxiv.org/abs/2306.06786
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a higher-order
Externí odkaz:
http://arxiv.org/abs/2303.17917