This paper investigates the Hamiltonian structure and Poisson bracket formulation of a higher-order, geometrically-exact Cosserat type beam with deforming cross-section in terms canonically conjugate variables.

The purpose of this department is to provide early announcement of significant new results, with some indications of proof. Although ordinarily a research announcement should be a brief summary of a paper to be published in full elsewhere, papers giving complete proofs of results of exceptional interest are also solicited. Manuscripts more than eight typewritten double spaced pages long will no...

We show that there is a generic transport of energy between the scalar field generated by the conformal transformation of higher order gravity theories and the matter component. We give precise relations of this exchange and show that, unless we are in a stationary spacetime, slice energy is not generically conserved. These results translate into statements about the relative behaviour of ordin...

Modeling music theories with computer programs has attracted composers and scholars for a long time. On the one hand, the resulting programs can serve as algorithmic composition tools. On the other hand, such an approach leads to a better understanding of existing as well as newly developed theories, which in turn can lead to a better understanding of music, as well as to better ways to retriev...

We generalize the lagrangian-hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a hamiltonian formalism for higher order lagrangian field theories, which does only depend on the action functional and, therefore, unlike previously proposed formalisms, is free from a...

Higher order curvature gravity has recently received a lot of attention due to the fact that it gives rise to cosmological models which seem capable of solving dark energy and quintessence issues without using “ad hoc” scalar fields. In this letter, a gravitational potential is obtained which differs from the Newtonian one because of a repulsive correction increasing with distance. We evaluate ...

We find an exact pp–gravitational wave solution of the fourth order gravity field equations. Outside the (delta–like) source this not a vacuum solution of General Relativity. It represents the contribution of the massive, m = (−β)−1/2, spin–two field associated to the Ricci squared term in the gravitational Lagrangian. The fourth order terms tend to make milder the singularity of the curvature ...

The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Sk...

In these lectures notes, we will discuss a particular higher order gravity theory, Lovelock theory, that generalises in higher dimensions than 4, general relativity. After briefly motivating modifications of gravity, we will introduce the theory in question and we will argue that it is a unique, mathematically sensible, and physically interesting extension of general relativity. We will see, by...

We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the vacuum case, solutions are found with closed, open and flat geometries, whilst the perfect fluid solutions are all spatially flat. Both early and late-time lim...