A theory of discrete Cosserat rods is formulated in the language of discrete Lagrangian mechanics. By exploiting Kirchhoff’s kinetic analogy, the potential energy density of a rod is a function on the tangent bundle of the configuration manifold and thus formally corresponds to the Lagrangian function of a dynamical system. The equilibrium equations are derived from a variational principle usin...

I briefly discuss effective Lagrangians for strong interactions while concentrating on two specific lagrangians for QCD at large matter density. I then introduce spectral duality in QCD a la Montonen and Olive. The latter is already present in QCD in the hadronic phase. However it becomes transparent at large chemical potential. Finally I show the relevance of having exact non perturbative cons...

In this paper I examine the breaking of internal symmetries from another point of view showing that is possible to reproduce the electroweak panorama of the traditional Standard Model in a exhaustive and self consistent way. The result is reached applying the main futures of the old Nambu-Jona Lasinio (NJL) mechanism to an electroweak invariant Lagrangian. In this context the use of functional ...

We consider the implications from the possibility that the recently observed state X(3872) is a meson-antimeson molecule. We write an effective Lagrangian consistent with the heavy-quark and chiral symmetries needed to describe X(3872) and study its properties.

We present a fluid particle model based on the Voronoi tessellation that allows one to represent an inviscid fluid in a Lagrangian description. The discrete model has all the required symmetries and structure of the continuum equations and can be understood as a linearly consistent discretization of Euler’s equations. Although the model is purely inviscid, we observe that the probability distri...

This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The ...

A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in mass Lagrangian coordinates. This analyses with cylindrical symmetry The medium is assumed inviscid thermally non-conducting. It modeled by a polytropic gas. Symmetries are found. cases finite infinite electric conductivity need to be analyzed separately. For $\sigma (\rho,p...

The Controlled Lagrangian method is a branch of energy shaping methods that is designed to control underactuated mechanical systems. The method emp...

The classical Lagrangian of chromodynamics, its quantization in the perturbation theory framework, and renormalization form the subject of these lectures. Symmetries of the theory are discussed. The dependence of the coupling constant αs on the renormalization scale μ is considered in detail.

We obtain, for a subclass of structure functions characterizing a first class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge parameters. We apply this to a nontrivial Hamiltonian system involving two primary constraints, as well as two secondary constraints of the Nambu-Goto type. ema...