Related papers: Geometric properties of Lagrangian mechanical syst…
Some aspects of the geometry and the dynamics of generalized Chaplygin systems are investigated. First, two different but complementary approaches to the construction of the reduced dynamics are reviewed: a symplectic approach and an…
We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…
We formulate $\mathcal{N}=2$ global supersymmetric Lagrangians of self-interacting vector multiplets in terms of variant multiplets, whose non-propagating fields are replaced with gauge three-forms. Setting the three-forms on-shell results…
In this paper, using diffusion processes, we compute the evolution equation on the manifold of Riemannian metrics for the Lagrangian induced by the $L^2$ stochastic kinetic energy functional.
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations…
A method to construct a geometric structure with the same solutions as a given variational principle is presented. The method applies to large families of variational principles. In particular, the known results that assign cosymplectic…
A new description, different by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and important results are obtained. We present…
We study two related invariants of Lagrangian submanifolds in symplectic manifolds. For a Lagrangian torus these invariants are functions on the first cohomology of the torus. The first invariant is of topological nature and is related to…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
Projective geodesic extensions are reparametrizations of the trajectories of a nonholonomic mechanical system (with only a kinetic energy Lagrangian), in such a way that they can be interpreted as part of the geodesics of a Riemannian…
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…
A Lie system is the non-autonomous system of differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional Lie algebra of vector fields, a so-called Vessiot--Guldberg Lie…
The calculation of the standard model Lagrangian of classical field theory within the framework of noncommutative geometry is sketched using a variant with 18 parameters. Improvements compared with the traditional formulation are contrasted…
Within the framework of phenomenological Lagrangians we construct the effective action of QCD relevant for the study of semileptonic decays of charmed mesons. Hence we evaluate the form factors of D -> P(0^-) l^+ nu_l at leading order in…
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural)…
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
Lagrangian coherent structures (LCSs) are material surfaces that shape finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from…