Filtered Leapfrog Time Integration with Enhanced Stability Properties

The Leapfrog method for the solution of Ordinary Differential Equation initial value problems has been historically popular for several reasons. The method has second order accuracy, requires only one function evaluation per time step, and is non-dissipative. Despite the mentioned attractive properties, the method has some unfavorable stability properties. The absolute stability region of the method is only an interval located on the imaginary axis, rather than a region in the complex plane. The method is only weakly stable and thus exhibits computational instability in long time integrations over intervals of finite length. In this work, the use of filters is examined for the purposes of both controlling the weak instability and also enlarging the size of the absolute stability region of the method.

Overview of Earth-Moon Transfer Trajectory Modeling and Design

TheMoon is the only celestial body that human beings have visited.The design of the Earth-Moon transfer orbits is a critical issue in lunar exploration missions.In the 21st century,new lunar missions including the construction of the lunar space station,the permanent lunar base,and the Earth-Moon transportation network have been proposed,requiring low-cost,expansive launch windows and a fixed arrival epoch for any launch date within the launch window.The low-energy and low-thrust transfers are promising strategies to satisfy the demands.This review provides a detailed landscape of Earth-Moon transfer trajectory design processes,from the traditional patched conic to the state-of-the-art low-energy and low-thrust methods.Essential mechanisms of the various utilized dynamic models and the characteristics of the different design methods are discussed in hopes of helping readers grasp thebasic overviewof the current Earth-Moon transfer orbitdesignmethods anda deep academic background is unnecessary for the context understanding.

Stability of weak solutions to climate dynamics model with effects of topography and non-constant external force

In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of the atmosphere, was considered.Under certain assumptions imposed on the initial data and by using some delicate estimates and compactness arguments, we proved the L^1-stability of weak solutions to the atmospheric equations.

The stability of a novel weakly alkaline slurry of copper interconnection CMP for GLSI

Chemical mechanical polishing（CMP） is one of the important machining procedures of multilayered copper interconnection for GLSI, meanwhile polishing slurry is a critical factor for realizing the high polishing performance such as high planarization efficiency, low surface roughness. The effect of slurry components such as abrasive（colloidal silica）, complexing agent（glycine）, inhibitor（BTA） and oxidizing agent（H_2O_2） on the stability of the novel weakly alkaline slurry of copper interconnection CMP for GLSI was investigated in this paper. First, the synergistic and competitive relationship of them in a peroxide-based weakly alkaline slurry during the copper CMP process was studied and the stability mechanism was put forward. Then 1 wt% colloidal silica, 2.5 wt% glycine,200 ppm BTA, 20 m L/L H_2O_2 had been selected as the appropriate concentration to prepare copper slurry, and using such slurry the copper blanket wafer was polished. From the variations of copper removal rate, root-mean square roughness（Sq） value with the setting time, it indicates that the working-life of the novel weakly alkaline slurry can reach more than 7 days, which satisfies the requirement of microelectronics further development.

IMPROVED COVARIANCE DRIVEN BLIND SUBSPACE IDENTIFICATION METHOD

An improved covariance driven subspace identification method is presented to identify the weakly excited modes. In this method, the traditional Hankel matrix is replaced by a reformed one to enhance the identifiability of weak characteristics. The robustness of eigenparameter estimation to noise contamination is reinforced by the improved Hankel matrix, in combination with component energy index （CEI） which indicates the vibration intensity of signal components, an alternative stabilization diagram is adopted to effectively separate spurious and physical modes. Simulation of a vibration system of multiple-degree-of-freedom and experiment of a frame structure subject to wind excitation are presented to demonstrate the improvement of the proposed blind method. The performance of this blind method is assessed in terms of its capability in extracting the weak modes as well as the accuracy of estimated parameters. The results have shown that the proposed blind method gives a better estimation of the weak modes from response signals of small signal to noise ratio （SNR）and gives a reliable separation of spurious and physical estimates.

LIPSCHITZ STABILITY OF GENERAL CONTROL SYSTEMS

Necessary and sufficient conditions for the new concepts of Lipschitz stability, Lipschitz weak stability and Lipschitz asymptotic stability of closed set for general control systems are given, using Liapunov-like functions.

LIPSCHITZ STABILITY OF DYNAMICAL SYSTEMS IN TERMS OF TWO MEASURES

Coyeptes of (h0,h) - (Lipschitz stability, (h0, h) -Lipschitz (weakly) asymptotic stability are introduced for dynamical sytems. Necessary and sufficient conditions are given respectively.

LIPSCHITZ STABILITY OFGENERAL CONTROL SYSTEMS Ⅱ.IN TERMS OF TWO MEASURES

The unified necessary and sufficient conditions for the new notions of (h0, h)-Lipschitz (weak) stability, (h0, h)-Lipschitz asymptotic stability of G.C.S. are given, using Liapunov-like functions.

Trajectory optimization for the Horyu-VI international lunar mission

The Horyu-VI nano-satellite is an international lunar mission with the purpose of studying the lunar horizon glow(LHG)—a still unclear phenomenon caused by electrostatically charged lunar dust particles.This study analyzes the mission trajectory with the hypothesis that it is launched as a secondary payload of the NASA ARTEMIS-II mission.In particular,the effect of the solar gravity gradient is studied;in fact,depending on the starting relative position of the Moon,the Earth,and the Sun,the solar gradient acts differently on the trajectory—changing it significantly.Therefore,the transfer and lunar capture problem is solved in several cases with the initial Sun–Earth–Moon angle as the key parameter.Furthermore,the inclination with respect to the Moon at capture is constrained to be equatorial.Finally,the problem of stabilization and circularization of the lunar orbit is addressed in a specific case,providing an estimate of the total propellant cost to reach the final orbit around the Moon.

ON THE SOLVABILITY OF GENERAL LINEAR METHODS FOR DISSIPATIVE DYNAMICAL SYSTEMS

The main purpose of the present paper is to examine the existence and local uniqueness of solutions of the implicit equations arising in the application of a weakly algebraically stable general linear methods to dissipative dynamical systems, and to extend the existing relevant results of Runge-Kutta methods by Humphries and Stuart(1994). [ABSTRACT FROM AUTHOR]