We derive the Euler-Lagrange equations for nonlinear elastic rods with self-contact. The excluded volume constraint is formulated in terms of an upper bound on the global curvature of the centreline. This condition is shown to guarantee the global injectivity of the deformation mapping of the elastic rod. Topological constraints such as a prescribed knot and link class to model knotting and sup...

Many models of three-dimensional rigid body dynamics employ Euler parameters as rotational coordinates. Since the four Euler parameters are not independent, one has to consider the quaternion constraint in the equations of motion. This is usually done by the Lagrange multiplier technique. In the present paper, various forms of the rotational equations of motion will be derived, and it will be s...

In this Comment, we point out that the Euler-Lagrange equations, which are referred to as the general equilibrium equations by Zhao et al. [Phys. Rev. E 74, 032801 (2006)] are incorrect along with the equations which are derived from them. The correct equations are provided in this Comment. We produce new numerical results with the use of the correct equations.

Let X be a closed smooth 4-manifold. In the Theory of the SeibergWitten Equations, the configuration space is Cα = Aα × Γ (S + α ), where Aα is a space of u1-connections defined on a complex line bundle over X and Γ (S α ) is the space of sections of the positive complex spinor bundle over X. The original SWα-equations are 1 -order PDE fitting into a variational principle SWα : Aα × Sα → R, whi...

This paper provides the explicit expression of investment facing a binding debt ceiling and the explicit expression of the Lagrange multipliers related to the binding debt ceiling constraint. This result allows us to check for misspecification of the parameterizations of these Lagrange multipliers used in Euler investment equations tests during the 1990’s.  2000 Elsevier Science S.A. All right...

Using the subgroup structure of the generalized Poincaré group P (1, 4), the symmetry reduction of the five-dimensional wave and Dirac equations and Euler–Lagrange– Born–Infeld, multidimensional Monge–Ampere, eikonal equations to differential equations with a smaller number of independent variables is done. Some classes of exact solutions of the investigated equations are constructed.

It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial differential equations. These include numerous systems of physical interest, in particular, those for various material media in general relativity. There is prov...

This report provides additional results on local region statistics and accompanies the work in [2]. In particular, we derive the Euler-Lagrange equations of the local Gaussian region model including variance as well as the local nonparametric model. Moreover, we show some experimental results on contour tracking with local region statistics. 1 Euler-Lagrange Equations for Local Region Statistic...