During the Deepwater Horizon (DWH) blowout, photooxidation of surface oil led to formation persistent photooxidized compounds, still found in shoreline sediments a decade later. Studies demonstrated that modified both biodegradation rates and effectiveness aerial dispersant applications. Despite significant consequences this weathering pathway, lack measurements prevented be accounted for DWH b...

It is shown that the Lagrange’s equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

Remark. Beauville proves that a Lagrangian fibration is a complete integrable system in [2, Proposition 1]. Thus, a general fibre of a fibre space of a projective irreducible symplectic manifold is an abelian variety. Remark. Markshevich states in [4, Remark 3.2] that there exists an irreducible symplectic manifold which has a family of non lagrangian tori. But this family does not form fibration.

We prove a Lagrangian analogue of the Conley conjecture: given a 1-periodic Tonelli Lagrangian with global flow on a closed configuration space, the associated EulerLagrange system has infinitely many periodic solutions. More precisely, we show that there exist infinitely many contractible periodic solutions with a priori bounded mean action and unbounded integer period.

This paper investigates a class of Lagrangian control systems with n degrees-offreedom (DOF) and n − 1 actuators, assuming that n − 1 virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds. The reduced dynamics of such systems are described by a second-order unforced differential equation. We present necessary and sufficient conditions under which ...

The present lecture notes address three columns on which the Lagrangian perturbation approach to cosmological dynamics is based: 1. the formulation of a Lagrangian theory of self–gravitating flows in which the dynamics is described in terms of a single field variable; 2. the procedure, how to obtain the dynamics of Eulerian fields from the Lagrangian picture, and 3. a precise definition of a Ne...

A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is derived from the d’Alambert-Lagrange principle for anholonomic constrained systems. A geometrical (coordinate-independent) formulation of the variational pr...