44 citations · 163 across the 19 of their papers we have counts for
21 papers
Presymplectic integrators for optimal control problems via retraction maps
María Barbero Liñán, David Martín de Diego
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.…
Variational integrators for non-autonomous systems with applications to stabilization of multi-agent formations
Leonardo Colombo, Manuela Gamonal Fernández, David Martín de Diego
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are a…
Nonholonomic Newmark method
Alexandre Anahory Simões, Sebastián J. Ferraro, Juan Carlos Marrero +1
Using the nonholonomic exponential map, we generalize the well-known family of Newmark methods for nonholonomic systems. We give numerical examples including a test problem where t…
Parallel iterative methods for variational integration applied to navigation problems
Sebastián J. Ferraro, David Martín de Diego, Rodrigo T. Sato Martín de Almagro
Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discr…
Contact bundle formulation of nonholonomic Maupertuis-Jacobi principle and a length minimizing property of nonholonomic dynamics
Alexandre Anahory Simoes, Juan Carlos Marrero, David Martín de Diego
We prove a nonholonomic version of the classical Mauper\-tuis-Jacobi principle which transforms an autonomous mechanical nonholonomic problem, determined by a kinetic minus potenti…
Local convexity for second order differential equations on a Lie algebroid
Juan Carlos Marrero, David Martín de Diego, Eduardo Martínez
A theory of local convexity for a second order differential equation (SODE) on a Lie algebroid is developed. The particular case when the SODE is homogeneous quadratic is extensive…