The optimal control problem for a class of hybrid systems (switched Lagrangian systems) is studied. Some necessary conditions of the optimal solutions of such a system are derived based on the assumption that there is a group of symmetries acting uniformly on the domains of different discrete modes, such that the Lagrangian functions, the guards, and the reset maps are all invariant under the a...

The Lagrangian predictability of general circulation models is limited by the need for high-resolution data streams to constrain small-scale dynamical features. Here velocity observations from Lagrangian drifters deployed in theGulf ofMexico during the summer 2012GrandLagrangianDeployment (GLAD) experiment are assimilated into the Naval Coastal Ocean Model (NCOM) 4D variational (4DVAR) analysis...

In this paper we consider an alternative approach to “un-reduction”. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have call...

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincaré equations in a new fashion and we show...

We study the homogenization of a class of actions with an underlying Lagrangian L defined on the set of absolutely continuous paths in the Wasserstein space Pp(R). We introduce an appropriate topology on this set and obtain the existence of a Γ-limit of the rescaled Lagrangians. Our main goal is provide to a representation formula for these Γ-limits in terms of the effective Lagrangians. Not on...

In this paper we consider a dynamical system which represents the model of the airplane flight in the vertical plane. The aim of this paper is to make some geometrical studies of the direct and inverse problems with concrete applications in the dynamical systems. It is studied the Lagrangian formalism for the inverse problem and we find a Lagrangian associated to this dynamical system. Next, we...

Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as pattern formation, population evolution and chemical reactions. In this paper we construct Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a coupled Lane-Emden system. Then the first integrals with respect to Noether and partial Noether operators are obt...

In this study, nonlinear vibration of a composite cable is investigated by considering nonlinear stress-strain relations. The composite cable is composed of an aluminum wire as reinforcement and a rubber coating as matrix. The nonlinear governing equations of motion are derived about to an initial curve and based on the fundamentals of continuum mechanics and the nonlinear Green-Lagrangian stra...

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multidimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statisti...