36 citations · 210 across the 58 of their papers we have counts for
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Unified formalism for the generalized kth-order Hamilton-Jacobi problem
Leonardo Colombo, Manuel de León, Pedro D. Prieto-Martínez +1
The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unifie…
Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Leonardo Colombo, Manuel de León, Pedro Daniel Prieto-Martínez +1
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formal…
Higher-order discrete variational problems with constraints
Leonardo Colombo, David Martín de Diego, Marcela Zuccalli
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric…
Lagrange-Poincaré reduction for optimal control of underactuated mechanical systems
Leonardo Colombo
We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lag…
Unified formalism for higher-order variational problems and its applications in optimal control
Leonardo Colombo, Pedro D. Prieto-Martínez
In this paper we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bu…
Lagrangian mechanics on centered semi-direct product
Leonardo J. Colombo, Henry O. Jacobs
There exists two types of semi-direct products between a Lie group and a vector space . The left semi-direct product, , can be constructed when is equipped…