Zobrazeno 1 - 10
of 74
pro vyhledávání: '"Zuccalli, Marcela"'
Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techn
Externí odkaz:
http://arxiv.org/abs/2411.00110
In this paper we work, first, with forced discrete-time mechanical systems on the configuration space $Q$ and construct closed $2$-forms $\omega^+$ and $\omega^-$ on $Q \times Q$, that are symplectic if and only if the system is regular. For a specia
Externí odkaz:
http://arxiv.org/abs/2403.05305
Publikováno v:
J. Phys. A: Math. Theor.(2023) 56 355202
In this paper we propose a process of Lagrangian reduction and reconstruction for symmetric discrete-time mechanical systems acted on by external forces, where the symmetry group action on the configuration manifold turns it into a principal bundle.
Externí odkaz:
http://arxiv.org/abs/2307.13167
This paper presents a reduction procedure for nonholonomic systems admitting suitable types of symmetries and conserved quantities. The full procedure contains two steps. The first (simple) step results in a Chaplygin system, described by an almost s
Externí odkaz:
http://arxiv.org/abs/2207.02251
Publikováno v:
Actas del XVI Congreso Antonio Monteiro 2021 (2023), pp. 119-128
In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is possible to reco
Externí odkaz:
http://arxiv.org/abs/2203.05600
Publikováno v:
J. Geom. Phys. (2022) 172,104417
In this work we study discrete analogues of an exact sequence of vector bundles introduced by M. Atiyah in 1957, associated to any smooth principal $G$-bundle $\pi:Q\rightarrow Q/G$. In the original setting, the splittings of the exact sequence corre
Externí odkaz:
http://arxiv.org/abs/2111.06843
Publikováno v:
Actas del XVI Congreso Antonio Monteiro. 2021 (2023), pp. 183-200
In this note we consider a few interesting properties of discrete connections on principal bundles when the structure group of the bundle is an abelian Lie group. In particular, we show that the discrete connection form and its curvature can be inter
Externí odkaz:
http://arxiv.org/abs/2109.08928
Publikováno v:
J. Geom. Mech., 12 (2020), 607-639
In this work we introduce a category $LDP_d$ of discrete-time dynamical systems, that we call discrete Lagrange--D'Alembert--Poincar\'e systems, and study some of its elementary properties. Examples of objects of $LDP_d$ are nonholonomic discrete mec
Externí odkaz:
http://arxiv.org/abs/2009.09582
In the Hamiltonian formalism, and in the presence of a symmetry Lie group, a variational reduction procedure has already been developed for Hamiltonian systems without constraints. In this paper we present a procedure of the same kind, but for the en
Externí odkaz:
http://arxiv.org/abs/1904.11645
In this paper we present a procedure to integrate, up to quadratures, the matching conditions of the energy shaping method. We do that in the context of underactuated Hamiltonian systems defined by simple Hamiltonian functions. For such systems, the
Externí odkaz:
http://arxiv.org/abs/1810.00620