We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler-Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as exp...

In a typical adaptive update law, the rate of adaptation is generally a function of the state feedback error. Ideally, the adaptive update law would also include some feedback of the parameter estimation error. The desire to include some measurable form of the parameter estimation error in the adaptation law resulted in the development of composite adaptive update laws that are functions of a p...

We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudo-differential equation with a scalar constraint. The structural properties of this formulation, which arises as the Euler-...

The purpose of the present paper is to establish the validity of the Euler–Lagrange equation for the solution x̂ to the classical problem of the calculus of variations.  2004 Elsevier Inc. All rights reserved.

This paper investigates virtual holonomic constraints for Euler-Lagrange systems with n degreesof-freedom and n− 1 controls. In our framework, a virtual holonomic constraint is a relation specifying n − 1 configuration variables in terms of a single angular configuration variable. The enforcement by feedback of such a constraint induces a desired repetitive behavior in the system. We give condi...

In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian L(x(t), where aD α t x(t)) and 0 < α < 1, such that the following is the corresponding Euler-Lagrange tD α b ( c aD α t )x(t) + b(t, x(t))( c aD α t x(t)) + f(t, x(t)) = 0. (1) At last, exact solutions for some Euler-Lagrange equations ar...

In this paper we present a variational formulation of the problem of determining the elastic stresses in a contact lens on an eye and the induced suction pressure distribution in the tear film between the eye and the lens. This complements the force-balance derivation that we used in earlier work [K. L. Maki and D. S. Ross, J. Bio. Sys., 22 (2014), pp. 235–248]. We investigate the existence of ...

This paper addresses the classical and discrete Euler-Lagrange equations for systems of n particles interacting quadratically in R. By highlighting the role played by the center of mass of the particles, we solve the previous systems via the classical quadratic eigenvalue problem (QEP) and its discrete transcendental generalization. The roots of classical and discrete QEP being given, we state ...

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 ...

I show that the general implicit-function problem (or parametrized fixedpoint problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this formula for both analytic functions and formal power series.