A novel procedure to reduce by four the order of Euler–Lagrange equations associated to n-th order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two C∞symmetries is established. The method is based on a pair of variational C∞-symmetries whose commutators satisfy a certain solvability condition. It allows one to recover...

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...

in this paper, we use petrov-galerkin elements such as continuous and discontinuous lagrange-type k-0 elements and hermite-type 3-1 elements to find an approximate solution for linear fredholm integro-differential equations on $[0,1]$. also we show the efficiency of this method by some numerical examples

The mathematical model of an industrial robot is usually described in the form of Lagrange-Euler equations, Newton-Euler equations or generalized d’Alambert equations. However, these equations require the physical parameters of a robot that are difficult to obtain. In this paper, two methods for calculation of a Lagrange-Euler model of robot using neural networks are presented and compared. The...

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...

In this paper, we suggest a new technique which uses Lagrange polynomials to get derivative-free iterative methods for solving nonlinear equations. With the use of the proposed technique and Steffens on-like methods, a new optimal fourth-order method is derived. By using three-degree Lagrange polynomials with other two-step methods which are efficient optimal methods, eighth-order methods can b...

We summarise research reported in (Efroimsky 2002, 2003; Efroimsky & Goldreich 2003a,b) and develop its application to planetary equations in non-inertial frames. Whenever a standard system of six planetary equations (in the Lagrange, Delaunay, or other form) is employed, the trajectory resides on a 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements ...

Abstract. The mathematical model of industrial robot is well known for example in the form of Lagrange-Euler equations, Newton-Euler equations or generalized d’Alambert equations. However, these equations require the physical parameters of robot like masses, inertia momentums, etc. that are very hard to measure. In the paper, the method for calculation of Lagrange-Euler robot model using neural...