The present article addresses the topic of grid motion computation in Arbitrary Lagrange–Euler (ALE) simulations, where a fluid mesh must be updated to follow displacements Lagrangian boundaries. A widespread practice is deduce for internal nodes from parabolic equation, such as harmonic introducing an extra computational cost solver. An alternative strategy proposed minimize that by changing e...

In this paper we present a calculus algorithm for the study of the compressible fluid’s stationary motion through profile grids, on an axial–symmetric flow–surface, in variable thickness of stratum. We show the applicability of the boundary element method (BEM) with real values, and the possibility of solving the integral equation of the velocity potential by using the successive approximation ...

Abstract A method for constructing general null Lagrangians and their higher harmonics is presented dynamical systems with one degree of freedom. It shown that these can be used to obtain non-standard Lagrangians, which give equations motion the law inertia some dissipative systems. The necessary condition deriving by using presented, it demonstrated this plays same role as Euler–Lagrange equat...

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the the giant galactical gyroscope. The Lorentz equation and the Bargmann-MichelTelegdi equations are generalized for the rotati...

In this paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function.   The general solution of the equation of motion is obtained, which satisfies the required radiation condition.  The appropriate traction free boundary conditions are also satisfied by the solution to obtain the required secular equation for...

Abstract To avoid the failure under longitudinal, shear, and mixed wave from earthquake, an archetypal vibration isolator based on a smooth discontinuous (SD) oscillator is proposed. This model comprises lumped mass mounted by vertical spring horizontal elastic continuum, which separately provides positive negative stiffness forming stable quasi-zero (SQZS) in all directions. The equation of mo...

This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane’s methods. Euler-Bernoulli beam theory is considered for modeling the intermediate flexible link. Based...

We introduce a “nonlinear” version of the Hamiltonian formalism which allows a self-consistent description of theories with degenerate Lagrangian. A generalization of the Legendre transform to the case when the Hessian is zero is done using the mixed (envelope/general) solutions of the multidimensional Clairaut equation. The corresponding system of equations of motion is equivalent to the Lagra...

We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. For noncommutative φ⋆4 scalar field theory, we derive its energy-momentum tensor from translation transformation and Lagrange field equation. We generalize the Heisenberg and quantum motion equations to the form of Moyal star-products for noncommutative...