We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description. Whether a given set of equations of motion admits or not a Lagrangian formulation has been an interesting issue for a long time. As early as 1887, Helmholtz formulated necessary and sufficient conditions for this to happen, and the problem has a rich history [1]. More recentl...

We examine the problem of defining Lagrangian and Hamiltonian mechanics for a particle moving on a quantum plane Qq,p. For Lagrangian mechanics, we first define a tangent quantum plane TQq,p spanned by noncommuting particle coordinates and velocities. Using techniques similar to those of Wess and Zumino, we construct two different differential calculi on TQq,p. These two differential calculi ca...

The idea of multiport systems has been known as a useful tool when regarding a system as an interconnection of physical elements throughout principle of power invariance, which has been widely used in electrical circuits and networks (see, for instance, [4, 14]), where the principle of power invariance is known as Tellegen’s theorem in electrical network theory (see [6]). From the viewpoint of ...

An improved Lagrangian relaxation (LR) solution to the thermal unit commitment problem (UCP) is proposed in this paper. The algorithm is characterized by: (1) a new Matlab function to determine the optimal path of the dual problem, (2) new initialization procedure of Lagrangian multipliers, based on both unit and time interval classification, (3) a flexible adjustment of Lagrangian multipliers,...

We construct, for a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the ‘fundamental Lepage equivalent’ associated with first-order Lagrangians defined on jets of sections of a fibred manifold.

We study the existence of closed characteristics on three-dimensional energy manifolds of second-order Lagrangian systems. These manifolds are always noncompact, connected, and not necessarily of contact type. Using the specific geometry of these manifolds, we prove that the number of closed characteristics on a prescribed energy manifold is bounded below by its second Betti number, which is ea...

[1] Motivated by increases in the realism of OGCMs and the number of drifting buoys in the ocean observing system, a new Lagrangian assimilation technique is implemented in an idealized, reduced-gravity configuration of the layered primitive equation model MICOM. Using an extensive set of twin experiments, the effectiveness of the Lagrangian observation operator and of a dynamical balancing tec...

We study the Born-Infeld equation from a Lagrangian point of view emphasizing the duality symmetry present in such systems. We obtain the Hamiltonian formulation directly from the Lagrangian. We also show that this system admits a dispersionless nonstandard Lax representation which directly leads to all the conserved charges (including the ones not previously obtained). We also present the gene...

We discuss how the existence of a regular Lagrangian description on the tangent bundle T Q of some configuration space Q allows for the construction of a linear structure on T Q that can be considered as " adapted " to the given dynamical system. The fact then that many dynamical systems admit alternative Lagrangian descriptions opens the possibility to use the Weyl scheme to quantize the syste...