We recall the notion of a nonholonomic system by means of an example of classical mechanics, namely the vertical rolling disk. For a general mechanical system with nonholonomic constraints, we present a Lagrangian formulation of the nonholonomic and vakonomic dynamics using the method of anholonomic frames. We use this approach to deal with the issue of when a nonholonomic system can be interpr...

This paper presents the Euler–Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the RiemannLiouville fractional derivative.

A new type of non-Abelian generalization of the Born-Infeld action is proposed, in which the spacetime indices and group indices are combined. The action is manifestly Lorentz and gauge invariant. In its power expansion, the lowest order term is the Yang-Mills action and the second term corresponds to the bosonic stringy correction to this action. Solutions of the Euler-Lagrange equation for th...

This paper has a very modest scope: we present our “operational system” for Hamiltonian mechanics on cotangent bundles M = T Q, based on moving frames. In a related work [10], we will present some concrete examples to convey the algorithmical nature of this formalism. A powerful tool in riemannian geometry is the “method of moving frames”, introduced by Élie Cartan. Actually, moving frames appe...

This article describes the design, modeling and identification of the main hydrodynamic parameters of an underwater glider vehicle is presented. The equations describing the dynamics of the vehicle is obtained from the Euler-Lagrange method. The main hydrodynamic parameters were obtained considering the geometry of the vehicle and its operating characteristics. Finally, simulation open loop sys...

Cosmological solutions of gravity coupled to scalar fields, with arbitrary scalar potential, were recently shown to be geodesics in an appropriately augmented, and conformally rescaled, target space. Here we obtain these geodesics as solutions of the Euler-Lagrange equations of a relativistic particle action. As an application, we find some exact (flat and curved) cosmologies for models with N ...

The Euler-Lagrange equations for some class of gravitational actions are calculated by means of Palatini principle. Polynomial structures with Einstein metrics appear among extremals of this variational problem.

The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function.

Abstract. We study vesicles formed by lipid bilayers that are governed by an elastic bending energy and on which the lipids laterally separate forming two different phases. The energy laden phase interfaces may be modeled as curves on the hyper-surface representing the membrane (sharp interface model). The phase field methodology is another powerful tool to model such phase separation phenomena...

In the present note, we give a simple general proof for the existence of solutions of the following two types of variational problems: PROBLEM A. To minimize fa F(x> u, • • • , Du)dx over a subspace VofW>*(tt). PROBLEM B. TO minimize ƒ« F(x, w, • • • , Du)dx for u in V with / a G(x, u, • • • , D^u)dx^c. The solution of the first problem yields a weak solution of a corresponding elliptic boundar...