The Teukolsky equation has long been known to lead to divergent integrals when it is used to calculate the gravitational radiation emitted when a test mass falls into a black hole from infinity. Two methods have been used in the past to remove those divergent integrals. In the first, integrations by parts are carried out, and the infinite boundary terms are simply discarded. In the second, the ...

In the Lagrangian framework for symmetries and conservation laws of field theories, we investigate globality properties of conserved currents associated with non–global Lagrangians admitting global Euler–Lagrange morphisms. Our approach is based on the recent geometric formulation of the calculus of variations on finite order jets of fibered manifolds in terms of variational sequences.

We give twenty eight diverse proofs of the fundamental Euler sum identity ζ(2, 1) = ζ(3) = 8 ζ(2, 1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating the wide variety of techniques fruitfully used to study such sums and the attraction of their study.

We establish a group-invariant version of the variational bicomplex that is based on a general moving frame construction. The main application is an explicit group-invariant formula for the Euler-Lagrange equations of an invariant variational problem.

We recall the notion of a nonholonomic system by means of an example of classical mechanics, namely the vertical rolling disk. For a general mechanical system with nonholonomic constraints, we present a Lagrangian formulation of the nonholonomic and vakonomic dynamics using the method of anholonomic frames. We use this approach to deal with the issue of when a nonholonomic system can be interpr...

This paper presents the Euler–Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the RiemannLiouville fractional derivative.

A new type of non-Abelian generalization of the Born-Infeld action is proposed, in which the spacetime indices and group indices are combined. The action is manifestly Lorentz and gauge invariant. In its power expansion, the lowest order term is the Yang-Mills action and the second term corresponds to the bosonic stringy correction to this action. Solutions of the Euler-Lagrange equation for th...

(2011) Convergence rate of numerical solutions to SFDEs with jumps. Strathprints is designed to allow users to access the research output of the University of Strathclyde. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. You may not engage in further distribution of the material for any profitmaking activities or any ...

This paper has a very modest scope: we present our “operational system” for Hamiltonian mechanics on cotangent bundles M = T Q, based on moving frames. In a related work [10], we will present some concrete examples to convey the algorithmical nature of this formalism. A powerful tool in riemannian geometry is the “method of moving frames”, introduced by Élie Cartan. Actually, moving frames appe...

This article describes the design, modeling and identification of the main hydrodynamic parameters of an underwater glider vehicle is presented. The equations describing the dynamics of the vehicle is obtained from the Euler-Lagrange method. The main hydrodynamic parameters were obtained considering the geometry of the vehicle and its operating characteristics. Finally, simulation open loop sys...