34 citations · 129 across the 10 of their papers we have counts for
10 papers
Regularity properties of fiber derivatives associated with higher-order mechanical systems
Leonardo Colombo, Pedro D. Prieto-Martínez
The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More pr…
Hamilton-Jacobi theory in multisymplectic classical field theories
Manuel de León, Pedro Daniel Prieto-Martínez, Narciso Román-Roy +1
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem…
Variational Principles for multisymplectic second-order classical field theories
Pedro Daniel Prieto-Martínez, Narciso Román-Roy
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and t…
A new multisymplectic unified formalism for second-order classical field theories
Pedro D. Prieto-Martínez, Narciso Román-Roy
We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds o…
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…
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…
Higher-order Mechanics: Variational Principles and other topics
Pedro D. Prieto-Martínez, Narciso Román-Roy
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical v…
Unified formalism for higher-order non-autonomous dynamical systems
Pedro D. Prieto-Martínez, Narciso Román-Roy
This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unifi…
Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
Pedro D. Prieto-Martínez, Narciso Román-Roy
The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for no…