Related papers: Routh reduction and Cartan mechanics
The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left…
This is a survey article, from the viewpoint of the completeness of the Marsden- Weinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi theory of the regular controlled Hamiltonian…
Linear programming relaxations are central to {\sc map} inference in discrete Markov Random Fields. The ability to properly solve the Lagrangian dual is a critical component of such methods. In this paper, we study the benefit of using…
We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional…
A new rotation version of the Curzon-Chazy metric is found. This new metric was obtained by means of a perturbation method, in order to include slow rotation. The solution is then proved to fulfill the Einstein field equations using a…
Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…
Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field…
This paper deals with the symmetry analysis of the Einstein Cartan theory which is an extension of the General Relativity and it accounts for the space-time torsion. We begin by applying Noether Theorem to the Lagrangian of the FRW type…
We review a range of reduction methods that have been, or may be useful for connecting models of the Earth's climate system of differing complexity. We particularly focus on methods where rigorous reduction is possible. We aim to highlight…
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions…
We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notion…
A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover,…
In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant-Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the space…
We argue that the non gauge invariant coupling between torsion and the Maxwell or Yang-Mills fields in Einstein-Cartan theory can not be ignored. Arguments based in the existence of normal frames in neighbourhoods, and an approximation to a…
The phase space path integral Wess-Zumino-Witten $\to$ Toda reductions are formulated in a manifestly conformally invariant way. For this purpose, the method of Batalin, Fradkin, and Vilkovisky, adapted to conformal field theories, with…
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor…
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 of systems. This model provides a straightforward and simple…
In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulum with fast rotation, weakly coupled $N$-oscillators with…
The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary…