The purpose of this paper is to construct a unified generating function involving the families higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using their functional equations, we investigate some properties these Moreover, derive several connected formulas relations including Miller–Lee polynomials, Laguerre Lagrange Hermite–Miller–Lee

The dynamics of randomly forced Burgers and Euler-Lagrange equations in S 1 × R d−1 in the case when there is only one one-sided minimizer in a compact subset of S 1 × R d−1 is studied. The existence of random invariant periodic minimizer orbits and periodicity of the stationary solution of the stochastic Burgers equations are obtained.

It is shown that the Lagrange’s equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.

In a recent paper [7] we interpreted configurational forces as necessary and sufficient dissipative mechanisms such that the corresponding Euler-Lagrange equations are satisfied. We now extend this argument for a dynamic elastic medium, and show that the energy flux obtained from the dynamic J integral ensures that the equations of motion hold throughout the body.

Since its inception more than 200 years ago, analytical mechanics has been continually drawn to the determination of the equations of motion for constrained mechanical systems. Following the fundamental work of Lagrange @1# who bequeathed to us the so-called Lagrange multipliers in the process of determining these equations, numerous scientists and mathematicians have attempted this central pro...

In this paper, we review two related aspects of field theory: the modeling fields by means exterior algebra and calculus, derivation dynamics, i.e., Euler-Lagrange equations, stationary action principle. contrast to usual tensorial these equations for theories, that gives separate components, coordinate-free forms are derived. These alternative reminiscent formulae vector expressed in terms der...

In the framework of geometrized first-order jet approach, we study the SyngeBeil generalized Lagrange jet structure, derive the canonic nonlinear and Cartan connections, and infer the Einstein-Maxwell equations with sources; the classical ansatz is emphasized as a particular case. The Lorentz-type equations are described and the attached Riemann-Jacobi structures for two certain uniparametric c...

We consider inverse problems for differential systems in the presence of random perturbations. By method additional variables, we establish sufficient conditions representation stochastic equations second order form Lagrange equations, as well first canonical equations. The obtained results are illustrated by specific examples.

Many algorithms for the modelling and calculation of the dynamics of rigid parallel manipulators already exist, and are based on two approaches: The Newton-Euler method and the Lagrangian principle. For the Newton-Euler method the dynamics equations are generated by the complete analysis of all forces and torques of each rigid body in the robot’s structure (Featherstone & Orin, 2000, Spong & Vi...

We consider geometric variational problems for a functional defined on a curve in a three-dimensional space. The functional is assumed to be written in a form invariant under the group of Euclidean motions. We present the Euler-Lagrange equations as equilibrium equations for the internal force and moment. Examples are discussed to illustrate our approach. This form of the equations particularly...