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We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Jacobi groupoids are introduced as a generalization of Poisson and contact groupoids and it is proved that generalized Lie bialgebroids are the infinitesimal invariants of Jacobi groupoids. Several examples are discussed. [Copyright &y& Elsevier]

Studies the geometric quantization of Jacobi manifolds. Natural cohomology on Jacobi manifolds; Characterization of the existence of prequantization bundles; Foliation of Jacobi manifolds; Lie algebra of Jacobi manifolds.

In this paper a description, a la Tulczyjew, of constrained time-dependent dynamical systems in terms of special symplectic manifolds is first developed. Next, this description is combined with the constraint algorithm for time-dependent constrained systems. [ABSTRACT FROM AUTHOR]

We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perpendicular to a principal axis of inertia of the body, then the reduced equations are integrable and, in the generic case, possess a smooth invariant measure. Interestingly, in this generic case, the first integral that permits integration is transcendental and the density of the invariant measure depends on the angular velocities. We also study the Painlevé property of the solutions. [ABSTRACT FROM AUTHOR]

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach. [ABSTRACT FROM AUTHOR]

Lichnerowicz–Jacobi cohomology of Jacobi manifolds is reviewed. The use of the associated Lie algebroid allows to prove that the Lichnerowicz–Jacobi cohomology is invariant under conformal changes of the Jacobi structure. We also compute the Lichnerowicz–Jacobi cohomology for a large variety of examples. [Copyright &y& Elsevier]

Studies the dynamics of generalized Poisson and Nambu-Poisson brackets. General brackets of functions defined for skew-symmetric contravariant tensors; Similarities and differences of the brackets; Characterization of Poisson morphisms and generalized Poisson automorphisms.

The aim of this paper is to develop a constraint algorithm for time-dependent Lagrangian systems which permit us to solve the motion equations. This algorithm extends the Gotay and Nester algorithm for autonomous Lagrangians which is, in fact, a particular case. To do this the almost stable tangent geometry of the evolution space and the notion of cosymplectic structure are used. [ABSTRACT FROM AUTHOR]

This work analyzes the integrated water vapor (IWV) measured at six Aerosol Robotic Network (AERONET) stations with nearby global navigation satellite system (GNSS) in the Iberian Peninsula for the period 2007–2018. It is shown that both instruments have a high correlation (R 2 > 0.91), with small mbe below 1.5 mm and standard deviation (SD) below 2 mm. However, some dependences have been observed when MBE and SD are represented in bins of three variables: IWV, solar zenith angle (SZA), and aerosol optical depth (AOD). The greater or lesser amount of water vapor in the atmosphere seemed to be the more influential variable, increasing dry bias and SD with increasing IWV. Moreover, high SZA values were related to SD increases. A clear seasonal cycle for Cimel–GNSS differences was observed which was mainly related to IWV seasonal cycle. Additionally, AOD did not show a remarkable influence on Cimel–GNSS differences. Finally, the monthly differences are also analyzed with metadata information about Cimel device ID numbers, showing that, for long-term studies, this information can be very valuable. • AERONET sun-photometer IWV data are compared against GNSS in the Iberian Peninsula. • Correlation is very high (R^2 > 0.91) with small MBE and SD. • Dependences are studied, being the more influential variable IWV. • Device-related and other metadata are valuable information for long term studies. [ABSTRACT FROM AUTHOR]

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces. [ABSTRACT FROM AUTHOR]