We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with...

The issue of different parameterizations of the axisymmetric vesicle shape addressed by Hu Jian-Guo and Ou-Yang Zhong-Can [ Phys.Rev. E 47 (1993) 461 ] is reassesed, especially as it transpires through the corresponding Euler Lagrange equations of the associated elastic energy functional. It is argued that for regular, smooth contours of vesicles with spherical topology, different parameterizat...

We introduce a variational principle for field theories, referred to as the HamiltonPontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then d...

Abstract. Let G be a Banach Lie group modeled on the Banach space, possibly infinite dimensional, E. In this paper first we introduce Euler-Lagrange equations on the Lie group G with potential and right invariant metric. Euler-Lagrange equations are natural extensions of the geodesic equations on manifolds and Lie groups. In the second part, we study the geometry of the mechanical system of a r...

The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.

The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (,) elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.

We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variasional...

We study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncomutative differential geometry. By virtue of this variational principle, we get the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical ...