This paper proposes three different distributedevent-triggered control algorithms to achieve leader-followerconsensus for a network of Euler-Lagrange agents. We firstlypropose two model-independent algorithms for a subclass ofEuler-Lagrange agents without the vector of gravitational po-tential forces. By model-independent, we mean that each agentcan execute its algorithm...

The Harten–Lax–van Leer scheme is popularly used in the CFD community. However, oscillations are observed from shock tube problems for stiffened gases when the adiabatic index is greater than 3. To understand this phenomenon, the dissipation effect of the scheme is evaluated quantitatively in terms of dissipation matrices. We have proven and numerically demonstrated that lack of positive defini...

an internal ballistics model has been developed for performance prediction of a solid propellant rocket motor. inthis model a 1-d unsteady euler equation with source terms is considered. the flow is assumed as a non-reacting mixture of perfect gases with space and time varying thermo physical properties. the governing equations in the combustion chamber are solved numerically by using the stege...

numerical analyses have shown that successful flow simulations and the accuracy of solution noticeably depend on the number of nodes used in computational meshing. a suitable meshing should have the capability of adapting with main flow parameters. because the number of total nodes that can be used in numerical simulation is limited, making such grid for complex flows is almost difficult, if it...

Abstract In this research, a compact combination of Chebyshev polynomials is created and used as spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method based on applying Petrov–Galerkin procedure to discretize differential problem into system linear algebraic equations with unknown expansion coefficients. Using efficient Gaussian elimination procedure,...

We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet l-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distrib...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper we introduce the generalized twisted q-Euler numbers E (α) Keywords: Euler numbers and polynomials, twisted q-Euler numbers and q-Euler polynomials, generalized twisted q-Euler numbers and polynomials, q-Euler ze...

For any finite simple graphG = (V,E), the discrete Dirac operator D = d+d∗ and the Laplace-Beltrami operator L = dd∗+d∗d = (d+d∗)2 = D2 on the exterior algebra bundle Ω = ⊕Ωk are finite v × v matrices, where dim(Ω) = v = ∑ k vk, with vk = dim(Ωk) denoting the cardinality of the set Gk of complete subgraphs Kk of G. We prove the McKean-Singer formula χ(G) = str(e−tL) which holds for any complex ...

The traditional method of establishing the stiffness matrix associated with an intervertebral joint is valid only for infinitesimal rotations, whereas the rotations featured in spinal motion are often finite. In the present paper, a new formulation of this stiffness matrix is presented, which is valid for finite rotations. This formulation uses Euler angles to parametrize the rotation, an assoc...

In this paper we derive the singularity-free dynamic equations of spacecraftmanipulator systems using a minimal representation. Spacecraft are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange’s equations. We circumvent these issues by introducing quasi-coordinates which allows us to der...