We use analytic continuation to derive the Euler-Lagrange equations associated to the Pfaffian in indefinite signature (p, q) directly from the corresponding result in the Riemannian setting. We also use analytic continuation to derive the Chern-Gauss-Bonnet theorem for pseudo-Riemannian manifolds with boundary directly from the corresponding result in the Riemannian setting. Complex metrics on...

In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler–Lagrange geodesics and Wong’s fractional equations are derived. Many interesting consequences are explored.

The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.

This paper considers the problem of designing explicit measurement feedback H∞ control laws for a class of Euler-Lagrange systems. For these systems the joint positions are assumed as outputs of the system, while velocity measures are to be estimated from an observer+controller structure. The main contribution of this work lies in the explicit formulation of the dynamic structure of a joined ob...

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.