Related papers: Unified Lagrangian-Hamiltonian formalism for conta…
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 non-autonomous first-order mechanical systems, as well as for…
In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of $k$-contact Hamiltonian systems, which is…
In this paper we present a unified Lagrangian--Hamiltonian geometric formalism to describe time-dependent contact mechanical systems, based on the one first introduced by K. Kamimura and later formalized by R. Skinner and R. Rusk. This…
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical…
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 unified formalism of Skinner and Rusk for these kinds of systems,…
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including…
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 version of the Variational Principles which allows us to…
In this paper we discuss singular Lagrangian systems on the framework of contact geometry. These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic…
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 unified Lagrangian-Hamiltonian formalism for the geometric…
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian…
We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, ${\rm…
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for…
We develop a Hamilton-Jacobi theory for singular lagrangian systems in the Skinner-Rusk formalism. Comparisons with the Hamilton-Jacobi problem in the lagrangian and hamiltonian settings are discussed.
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are…
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of…
Some mechanical systems with dissipation can be described within the framework of the so-called contact mechanics: a modified form of the Euler-Lagrange equations stemming from Herglotz's variational principle, which admits a geometric…
We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a…
In this paper, we introduce a geometric description of contact Lagrangian and Hamiltonian systems on Lie algebroids in the framework of contact geometry, using the theory of prolongations. We discuss the relation between Lagrangian and…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…