8 papers
Variational integrators using forced discrete Hamiltonian systems
M. I. Caruso, J. Fernandez, C. I. Tori +1
We study discrete Hamiltonian systems defined on cotangent bundles that are subjected to external forces, whose trajectories are determined by a discrete variational principle. We…
Lagrangian reduction of symmetric discrete mechanical systems: a survey
MatÃas I. Caruso, Javier Fernández, Cora Tori +1
In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we us…
Remarks on structures and preservation in forced discrete mechanical systems of Routh type
MatÃas I. Caruso, Javier Fernández, Cora Tori +1
We study a type of forced discrete mechanical system -- that we name of Routh type -- whose (discrete) time-flow preserves a symplectic structure on . That…
Lagrangian neural networks for nonholonomic mechanics
Viviana Alejandra Diaz, Leandro Martin Salomone, Marcela Zuccalli
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 sy…
Reduction of hybrid Hamiltonian systems with non-equivariant momentum maps
Leonardo Colombo, MarÃa Emma Eyrea Irazú, MarÃa Eugenia GarcÃa +2
We develop a reduction scheme à la Marsden-Weinstein-Meyer for hybrid Hamiltonian systems. Our method does not require the momentum map to be equivariant, neither to be preserved b…
Homogeneous bi-Hamiltonian structures and integrable contact systems
Leonardo Colombo, Manuel de León, MarÃa Emma Eyrea Irazú +1
Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator rel…