Singular lagrangian systems and variational constrained mechanics on Lie algebroids

The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard tangent bundles...). In particular, we are interested in two cases: singular Lagrangian systems and vakonomic mechanics (variational constrained mechanics). Several examples illustrate the interest of these developments.Comment: 42 pages, Section with examples improve

A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define an almost aff-Poisson bracket on the constraint AV-bundle, which plays a prominent role in the description of nonholonomic dynamics. Moreover, these developments give a general description of nonholonomic systems and the unified treatment permits to study nonholonomic systems after or before reduction in the same framework. Also, it is not necessary to distinguish between linear or affine constraints and the methods are valid for explicitly time-dependent systems.Comment: 50 page

Co-located wave and offshore wind farms: A preliminary approach to the shadow effect

In recent years, with the consolidation of offshore wind technology and the progress carried out for wave energy technology, the option of combine both technologies has arisen. This combination rest mainly in two main reasons: in one hand, to increase the sustainability of both energies by means of a more rational harnessing of the natural resources; in the other hand, to reduce the costs of both technologies by sharing some of the most important costs of an offshore project. In addition to these two powerful reasons there are a number of technology synergies between wave and wind systems which makes their combination even more suitable. Co-located projects are one of the alternatives to combine wave-wind systems, and it is specially for these project were so-called shadow effect synergy becomes meaningful. In particular, this paper deals with the co-location of Wave Energy Conversion (WEC) technologies into a conventional offshore wind farm. More specifically, an overtopping type of WEC technology was considered in this work to study the effects of its co-location with a conventional offshore wind park. This study aims to give a preliminary approach to the shadow effect and its implications for both wave and offshore wind energies

CO-LOCATED WAVE AND OFFSHORE WIND FARMS: A PRELIMINARY CASE STUDY OF AN HYBRID ARRAY

In recent years, with the consolidation of offshore wind technology and the progress carried out for wave energy technology, the option of co-locate both technologies at the same marine area has arisen. Co-located projects are a combined solution to tackle the shared challenge of reducing technology costs or a more sustainable use of the natural resources. In particular, this paper deals with the co-location of Wave Energy Conversion (WEC) technologies into a conventional offshore wind farm. More specifically, an overtopping type of WEC technology was considered in this work to study the effects of its co-location with a conventional offshore wind park