The Existence of Periodic Solutions of a Class of <i>n</i>-Degree Polynomial Differential Equations*

This paper deals with a class of n-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (n is an odd number) or two (n is an even number) periodic solutions of the equation is obtained. These conclusions have certain application value for judging the existence of periodic solutions of polynomial differential equations with only one higher-order term.

On the growth of transcendental entire solutions of algebraic differential equations

In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail.

Existence of Periodic Solutions for Generalized Liénard-Typed Functional Differential Equations

The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

PERIODIC SOLUTIONS OF THIRD-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions

Solvability for a Coupled System of Fractional p-Laplacian Differential Equations at Resonance

In this paper,by using the coincidence degree theory,the existence of solutions for a coupled system of fractional p-Laplacian differential equations at resonance is studied.The result obtained in this paper extends some known results.An example is given to illustrate our result.

Nonrecurrence Theorems of Periodic Solutions for Functional Differential Equations

nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.

PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST-ORDER INTEGRO-DIFFERENTIAL EQUATIONS OF MIXED TYPE

The existence of at feast one solution and the existence of extreme solutions of periodic boundary value problems for first-order integro-differential equations of mixed type are studied, in the presence of generalized upper and laver solutions. The discussion is based an new comparison theorems and coincidence degree and monotone iterative methods.

Existence of Periodic Solution for a Kind of Functional Differential Equation

In this paper,a kind of high order functional differential equation is considered.By using the theory of concidence degree,a sufficient condition of existence of at least one 2π-period solution is obtained.

Existence of Solutions of Three-Dimensional Fractional Differential Systems

In this article, we consider the three-dimensional fractional differential system of the form together with the Neumann boundary conditions,? where are the standard Caputo fractional derivatives, . A new result on the existence of solutions for a class of fractional differential system is obtained by using Mawhin’s coincidence degree theory. Suitable examples are given to illustrate the main results.

Numerical Modeling of a New Flight Simulator Enabling Continuous 360⁃Degree Spinning and Translational Motion

This paper presents a new nine⁃degree⁃of⁃freedom parallel mechanism,which can be applied as a flight simulator.The mechanism is composed by Stewart turntable and another three⁃axis turntable.The Stewart platform can realize six⁃degree⁃of⁃freedom movement in space,but the working space is limited.After the three⁃axis turntable is installed,the rotation space can be increased to simulate more realistic flight conditions.This paper analyzes the new flight simulator from kinematics and dynamics aspects.In addition,the flight simulator is simulated and analyzed based on the MATLAB/Simulink simulation system.The results obtained from the numerical simulations is planned to be used for the practical manufacturing and applications of the new platform.

球面2-DOF冗余驱动并联机器人静力学全解

以球面2-DOF冗余驱动并联机器人为研究对象,在考虑构件弹性的情况下,采用传统的拆杆法建立机构的静力学平衡方程,利用积分法求出各杆件变形,再运用小变形叠加原理建立机构的变形补充协调方程,共得到42个方程,但该机构为冗余机构,共有43个未知数,为此采用输入力优化方法,得到该机构静力学全解。通过数值算例,绘制输出轴在外载荷作用下沿给定轨迹的受力图。研究为该机构在工程中的结构设计与应用提供了静力学理论基础。

Numerical Simulation of a Planing Vessel at High Speed

Planing vessels are applied widely in civil and military situations.Due to their high speed,the motion of planning vessels is complex.In order to predict the motion of planning vessels,it is important to analyze the hydrodynamic performance of planning vessels at high speeds.The computational fluid dynamic method（CFD） has been proposed to calculate hydrodynamic performance of planning vessels.However,in most traditional CFD approaches,model tests or empirical formulas are needed to obtain the running attitude of the planing vessels before calculation.This paper presents a new CFD method to calculate hydrodynamic forces of planing vessels.The numerical method was based on Reynolds-Averaged Navier-Stokes（RANS） equations.The volume of fluid（VOF） method and the six-degrees-of-freedom equation were applied.An effective process was introduced to solve the numerical divergence problem in numerical simulation.Compared with experimental results,numerical simulation results indicate that both the running attitude and hydrodynamic performance can be predicted well at high speeds.

Existence of Solutions for Infinity-Point Nonlinear Fractional Boundary Value Problem at Resonance

A class of the boundary value problem for fractional order nonlinear differential equation with Riemann-Liouville fractional derivative on the half line was studied. By using the coincidence degree theory due to Mawhin and constructing the suitable operators,the existence theorem of at least one solution has been established. An example is given to illustrate our result.

SB模型恒稳定解的degree(英文)

研究一个非线性常微分方程系统———一个简化的Brusselator模型.证明这个模型存在一个严格的正的不变区域,在此区域内该模型存在唯一的恒稳定解,且解的degree为1.

Nonlinear suboptimal tracking control of spacecraft approaching a tumbling target

We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass（CM）, the kinematic coupling between translation and rotation is taken into consideration to directly describe the motion of the spacecraft＇s sensors or devices which are not coincident with the CM. Thus, a kinematically coupled 6 degrees-of-freedom（DOF） relative motion model for the instrument（feature point） is set up. To make the chaser spacecraft＇s feature point track the target＇s, an optimal tracking problem is defined and a control law with a feedback-feedforward structure is designed. With quasi-linearization of the nonlinear dynamical system, the feedforward term is computed from a specified constraint about the dynamical system and the reference model, and the feedback action is derived starting from the state-dependent Ricca equation（SDRE）. The proposed controller is compared with an existing suboptimal tracking controller, and numerical simulations are presented to illustrate the effectiveness and superiority of the proposed method.

INCREASING PROPERTY OF SPECTRUM IN THE VIBRATIONS OF A CYCLIC CHAIN OF MASSES DISTRIBUTED ACCORDING TO THE GTM SEQUENCE

Generalized Thue-Morse sequences were introduced into the vibrational problem of a chain of masses linked by springs of constant strength, and the increasing property of spectrum of linear operator about the vibrational model was proved.

Numerical Simulation about the Characteristics of the Store Released from the Internal Bay in Supersonic Flow

To understand the influence of the initial release conditions on the separation characteristics of the store and improve it under high Mach number(Ma=4)flight conditions,the overset grid method and the Realizable k−εturbulence model coupled with an equation with six degrees of freedom are used to simulate the store released from the internal bay.The motion trajectory and the attitude angle of the store separation under the conditions of different centroid,velocity,height and control measures are given by the calculated result.Through analysis,the position of the centroid will affect the separation of the store,which needs to be considered in the design.Increasing the launching height is conducive to the separation of the store.If the store has an initial velocity,it can leave the internal bay more quickly and reduce the probability of collision with the wall.Cylindrical rod and slanted aft wall control measures can improve the attitude of the store and make the store fall more smoothly.

基于改进麻雀优化PID的波浪补偿控制方法

随着海上风电“十四五”规划的不断推动,在深远海域对兆瓦级大功率海上风机的需求量随之增加,其规模也在不断扩大。但是,在吊运、安装等海上工作过程中,复杂海浪对船舶产生的持续影响导致风机安装的精度和效率大幅下降,甚至会对人员安全以及财产造成重大损失。在深远海域复杂海况下对工程船舶进行有效的波浪补偿,可提供稳定的作业环境以保证精准高效地完成各项工作,因此,本文提出了一种基于改进麻雀优化PID的波浪补偿控制方法并将其应用于Stewart补偿平台。首先,建立波浪补偿平台动力学以及运动学反解模型,并设计正解模型迭代求解算法。随后,使用PID进行波浪补偿控制,并通过麻雀搜索算法优化参数。接着,采用Circle混沌映射对其进行初始化分布,以解决初始化不均匀的问题;并采用动态自适应加权、柯西突变以及反向学习以提升算法全局寻优能力。最后,生成4~6级海况下的某工程船运动数据作为系统输入,利用MATLAB和Simulink软件平台搭建模型进行补偿控制验证,并在Stewart硬件平台上做补偿试验。结果表明,改进麻雀搜索算法具有较快的收敛速度、较高的精度和更好的寻优能力,优化后的PID控制方法更适合用于复杂海况下波浪补偿平台的控制优化,可为大功率海上风机安装的补偿平台控制系统设计提供参考。

Effect of Gaussian Noise Amplitude on Translation Error Estimated Using Double-Wayland Algorithm

The Wayland algorithm has been improved in order to evaluate the degree of visible determinism for dynamical systems that generate time series. The objective of this study is to show that the Double-Wayland algorithm can distinguish between time series generated by a deterministic process and those generated by a stochastic process. The authors conducted numerical analysis of the van der Pol equation and a stochastic differential equation as a deterministic process and a Ganssian stochastic process, respectively. In case of large S/N ratios, the noise term did not affect the translation error derived from time series data, but affected that from the temporal differences of time series. In case of larger noise amplitudes, the translation error from the differences was calculated to be approximately 1 using the Double-Wayland algorithm, and it did not vary in magnitude. Furthermore, the translation error derived from the differenced sequences was considered stable against noise. This novel algorithm was applied to the detection of anomalous signals in some fields of engineering, such as the analysis of railway systems and bio-signals.