73 citations · 670 across the 56 of their papers we have counts for
5 papers · 1 filter
Kinematic reduction and the Hamilton-Jacobi equation
María Barbero-Liñán, Manuel de León, Juan Carlos Marrero +2
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric i…
Discrete second-order Euler-Poincaré equations. Applications to optimal control
Leonardo Colombo, Fernando Jimenez, David Martin de Diego
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geo…
Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings
Manuel de Leon, Fernando Jimenez, David Martin de Diego
The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds o…
On the geometry of higher-order variational problems on Lie groups
Leonardo Colombo, David Martin de Diego
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and a…
Symplectic groupoids and discrete constrained Lagrangian mechanics
Juan Carlos Marrero, David Martín de Diego, Ari Stern
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of s…