评《非线性动力学(混沌理论)概要》一书

某些完全确定性的动力学系统，在没有任何外加的随机性扰动的情况下．便能出现与随机过程（如Ｂｒｏｗｎ运动）难以区分的动力学行为，这类现象被概括为一个在中西文化中渊源流长的词语：混沌．混饨等非线性动力学问题的探索，不仅是理论物理中的重要组成部分，而且它打破了学科界限，渗透到其他物理分支和物理学科之外的其他学科．在这种背景下，向理论物理之外的科技工作者普及混沌理论知识无疑是很必要的，并且已有一些尝试，而Ｒ．Ｌ．Ｉｎｇｒａｈａｍ的新著《非线性动力学（混沌理论）概要》［１］一书是其中颇有特色的一种．该书共分…     

三色彩色光栅的制造

本文叙述了彩色光栅的制造方法,该方法制造简单,且精度较高,并对彩色光栅制造工艺如何改进提出了看法。     

Variational principle and dynamical equations of discrete nonconservative holonomic systems

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler--Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.     

微分本构粘弹性轴向运动弦线横向振动分析的差分法

给出了微分本构粘弹性轴向运动弦线横向振动数值仿真的一种差分法．文中建立了具有微分本构的粘弹性运动弦线的横向振动模型;通过对系统的控制方程和本构方程在不同的分数节点离散,得到一种新的差分方法．利用这一方法,弦线振动方程的数值计算过程可以交替地显式进行,且有较小的截断误差和好的数值稳定性．与通用的方法比较,新的方法计算简单、方便．文中利用方程的不变量检验了数值结果的可靠性,并利用这一方法给出了一类弦线模型的参数振动分析．     

Solitons in a generalized (2+1)-dimensional Ablowitz－Kaup－Newell－Segur system

In the previous Letter (Zheng C L and Zhang J F 2002 Chin. Phys. Lett. 19 1399), a localized excitation of the generalized Ablowitz－Kaup－Newell－Segur (GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps, rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations, which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.     

Chaotic attitude motion of a magnetic rigid spacecraft

IntroductionAttitudedynamicsofspacecraftisascientificresearchsubjectwithgreatsignificance[1,2 ].Aschaosiswidelyanddeeplyinvestigated ,muchattentionhasbeenpaidonchaoticattitudemotionofspacecraft.Itnotonlyprovidesadefiniteengineeringbackgroundforexploringchaos,butalsooffersanewviewpointfordesigningspacecraft.Ithasbeenshownthatthereexistschaoticattitudemotioninsomemodelsofspacecraft,suchasspinningsatellitesinacircularorbit,gyrostatsatellitesinthegravitationalfield ,andtetheredsatellites[3 ,4].Ho…     

磁性刚体航天器的混沌姿态运动

研究在地球万有引力场和磁场中的磁性刚体航天器在圆轨道上的混沌姿态运动。利用动量矩原理建立了系统的动力学模型。应用Melnikov方法证明了存在复杂非游荡Cantor集。分别采用时间历程、功率谱、Poincaré映射和Liapunov指数对系统动力学行为进行了数值研究。数值仿真表明,随着磁场力矩的增强,系统准周期环面破裂而出现混沌。     

Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems

In this paper, we have extefided the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.     

Chaos in Perturbed Planar Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＭｅｌｎｉｋｏｖｍｅｔｈｏｄｆｏｒｄｅｔｅｃｔｉｎｇｃｈａｏｓ[1]ｈａｓｂｅｅｎｅｘｔｅｎｄｅｄｔｏｈｉｇｈ＿ｄｉｍｅｎｓｉｏｎａｌｓｙｓｔｅｍｓｗｉｔｈｓｌｏｗｌｙ＿ｖａｒｙｉｎｇａｎｇｌｅｐａｒａｍｅｔｅｒｓ ,ｂｕｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｕｎｐｅｒｔｕｒｂｅｄｉｎｔｅｇｒａｂｌｅｓｙｓｔｅｍｓａｒｅｒｅｑｕｉｒｅｄｔｏｂｅＨａｍｉｌｔｏｎｉａｎ[2 ].Ｆｏｒｐｅｒｔｕｒｂｅｄｐｌａｎａｒｎｏｎ＿Ｈａｍｉｌｔｏｎｉａｎｉｎｔｅｇｒａｂｌｅｓｙｓｔｅｍｓ,ｔｈ…     

非线性粘弹性板的失稳条件

研究了给定面内周期激励作用下简支各向同性均匀粘弹性板平衡失稀问题,板的材料特性由Leaderman非线性本构关系描述,将板的动力学方程进行（Galerkin截断得到简化数学模型为弱非线性系统,采用平均法得到系统的平均化方程,对平均化方程进行稳定性分析得到了板平衡失稳的解析条件,对原系统用数值仿真进行研究,数值结果表明,随着激励幅值的增加或粘弹性材料系数的减少,系统平衡点推失稳,激励幅值和粘弹性材料系数的临界值均与解析结果接近。