73 citations · 670 across the 56 of their papers we have counts for
5 papers · 1 filter
Completeness of Riemannian metrics: an application to the control of constrained mechanical systems
José Ángel Acosta, Anthony Bloch, David Martín de Diego
We introduce a mathematical technique based on modifying a given Riemannian metric and we investigate its applicability to controlling and stabilizing constrained mechanical system…
Symmetry Preservation in Hamiltonian Systems: Simulation and Learning
Miguel Vaquero, Jorge Cortés, David Martín de Diego
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…
A new perspective on symplectic integration of constrained mechanical systems via discretization maps
María Barbero Liñán, David Martín de Diego, Rodrigo T. Sato Martín de Almagro
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 retractio…
Higher-order retraction maps and construction of numerical methods for optimal control of mechanical systems
Alexandre Anahory Simoes, Maria Barbero Liñán, Leonardo Colombo +1
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.…
Discrete gradient methods for irreversible port-Hamiltonian systems
Alexandre Anahory Simoes, David Martín de Diego, Bernhard Maschke
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are p…