This paper introduces eecient and accurate algorithms for simulating the rotation of a three-dimensional rigid object and compares them to several prior methods. The paper considers algorithms which exactly preserve angular momentum and either closely preserve or exactly conserve energy. First, we introduce a second-order accurate method that incorporates a third-order correction; then a third-...

Schools play a vital role in creating a greener future. They will likely be the first place most students encounter determined efforts to conserve energy and water or to reduce waste. The method used in this article is comparative and matching method, by using ISO 14001, OHSAS 18001 and ISO 50001 standards.  Implementing energy management along with other standards is the main objective of pres...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified T...

the current study presents a new analytical method for buckling analysis of rectangular and annular beams made up of functionally graded materials with constant thickness and poisson’s ratio. the boundary conditions of the beam are assumed to be simply supported and clamped. the stability equations were obtained by using conservation of energy. the critical buckling load and first mode shape we...

on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...