第三体摄动分析解的一种表达式

在太阳系中,大行星、小行星和卫星（包括自然卫星和人造卫星）等对应的运动问题,都可以处理成受摄二体问题,而摄动源又多为第三体,作为第三体的摄动天体,有的比运动天体离中心天体近,有的则相反,前者称为内摄内体,全者则称为外摄天体,对一个具体的运动天体,可以同时出现这两个摄动天体,但是,只要运动天体与摄动天体的轨道都建立在以中心天体（质心）为坐标原点的同一坐标系内,那么在一定条件下（即除运动天体与摄动天体     

The autoparametric 3:2 resonance in conservative systems

In the resonance model, high‐frequency quasi‐periodic oscillations (QPOs) are supposed to be a consequence of nonlinear resonance between modes of oscillations occurring within the innermost parts of an accretion disk. Several models with a prescribed mode–mode interaction were proposed in order to explain the characteristic properties of the resonance in QPO sources. In this paper, we examine nonlinear oscillations of a system having a quadratic nonlinearity and we show that this case is particularly relevant for QPOs. We present a very convenient way how to study autoparametric resonances of a fully general system using the method of multiple scales. We concentrate to conservative systems and discuss their behavior near the 3:2 parametric resonance. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

周期径向荷载作用下圆弧格构拱动力稳定性分析

基于结构弹性稳定理论,根据能量法推导出以位移为基本未知量的圆弧格构拱总势能,从Hamilton原理出发,建立了考虑剪切变形的圆弧格构拱的动力稳定微分方程.利用Galerkin方法将其转化为二阶常微分Mathieu型参数共振方程,求得周期解所包围的动力不稳定区域,探讨了圆弧格构拱发生参数共振的动力稳定性问题,分析了缀条面...     

检波器数量对组合压噪能力的影响

根据组合压噪的有关理论,在其他因素不变的情况下,采用数量越多的检波器,组合压制干扰波的效果越好。这使得人们认为在施工中应该采用尽量多的检波器以提高资料的信噪比。但是通过分析组合中检波器数量对规则干扰波,随机干扰波以及耦合高频微震衰减的影响证明:在其他因素不变的情况下,线性等灵敏度组合增加到"γ_max+3"个检波器以后(其中γ_max=组合基距/最小干扰波视波长), 组合对于规则干扰波的衰减能力不再随着检波器数量的增加而显著提高。在组合基距确定的情况下,检波器数量越多,对随机干扰的衰减越明显(包括在组内距小于随机干扰相关半径的情况下);但是增加到一定数量后,衰减效果不再出现明显变化。检波器数量的多少对衰减耦合高频微震没有明显作用。同时指出,确定组合中合理的检波器数量要与组合的摆放形式相结合;组合图形不合理的情况下,增加检波器数量不会显著提高组合的压噪能力;灵敏度分布不合理,是导致组合压噪能力降低的重要原因。在线性等灵敏度组合的基础上,利用玫瑰图进行分析,可以确定工区面积组合(包括道间混波后)中使用的合理的检波器数量。     

珠江河口对外海潮波响应的固有频率研究——采用系统控制论方法

采用受控的自回归滑动平均模型(CARMA)分别研究了珠江河口洪、枯季对外海潮波响应的固有频率。枯季采用单输入单输出模型,洪季采用双输入单输出模型,通过验证、检验表明,模型(CARMA)可用于寻求复杂网河对外海潮波响应的固有频率,方法可靠,易操作。通过频率增益响应分析,发现枯季珠江河口的固有频率以浅水分潮频段为主,对应周期介于6~10.0 h之间,枯季固有频率未出现在全日潮波对应的频段。洪季珠江河口的固有频率也以浅水分潮频段为主,珠江河口对浅水分潮的系统增益响应幅值最大。固有频率接近浅水分潮频段的站点,枯季较洪季固有频率减小,对应周期延长。     

Propagating tsunami wave and subsequent resonant response signals detected by HF radar in the Kii Channel,Japan

Signals from the tsunami waves induced by the March 11, 2011 moment magnitude (M_w) 9.0 Tohoku-Oki earthquake and from subsequent resonances were detected as radial velocity variability by a high-frequency ocean surface radar (HF radar) installed on the eastern coast of the Kii Channel, at a range of about 1000 km from the epicenter along the eastern to southern coasts of Honshu Island. A time–distance diagram of band-passed (9–200 min) radial velocity along the beam reveals that the tsunami waves propagated from the continental shelf slope to the inner channel as progressive waves for the first three waves, and then natural oscillations were excited by the waves; and that the direction of the tsunami wave propagation and the axis of the natural oscillations differed from that of the radar beam. In addition, spectral analyses of the radial velocities and sea surface heights obtained in the channel and on the continental shelf slope suggest complex natural oscillation modes excited by the tsunami waves.     

Approximate Analytic Solutions of the Averaged Three-Body Problem at First-Order Resonance with Large Oblateness of the Central Planet

For the general spatial planetary three-body problem at first-order mean motion resonance under the large oblateness of the central planet, the analytic solutions of the averaged motion are obtained with the help of the Weierstrass functions accurate to the third-degree terms in the satellites' eccentricities and inclinations. The behavior of solutions is investigated on the phase plane.This revised version was published online in October 2005 with corrections to the Cover Date.     

A symplectic mapping model for the 3/4 exterior

We present a symplectic mapping model to study the evolution of a small body at the 3/4 exterior resonance with Neptune, for planar and for three dimensional motion. The mapping is based on the averaged Hamiltonian close to this resonance and is constructed in such a way that the topology of its phase space is similar to that of the Poincaré map of the elliptic restricted three-body problem. Using this model we study the evolution of a small object near the 3/4 resonance. Both chaotic and regular motions are found, and it is shown that the initial phase of the object plays an important role on the appearance of chaos. In the planar case, objects that are phase-protected from close encounters with Neptune have regular orbits even at eccentricities up to 0.44. On the other hand objects that are not phase protected show chaotic behaviour even at low eccentricities. The introduction of the inclination to our model affects the stable areas around the 3/4 mean motion resonance, which now become thinner and thinner and finally at is=10° the whole resonant region becomes chaotic. This may justify the absence of a large population of objects at this resonance.     

Dynamical causes of asymmetry in the arrangement of gaps in the asteroid belt

The centers of the gaps observed in the asteroid belt are displaced toward Jupiter from their positions that correspond to the exact commensurability between the mean motions of an asteroid and Jupiter. Using the current theory of stability and nonlinear oscillations of Hamiltonian systems, we point out the dynamical causes of this asymmetry. Our analysis is performed in terms of the plane circular restricted three-body problem. The orbits that correspond to Poincaré periodic solutions of the first kind are taken as unperturbed asteroid orbits.     

近地小行星轨道演化的研究

主要阐述近年来在近地小行星轨道演化研究工作中所获得的一些基本结果，即合理的力学模型和相应的有效算法，并以实际预报算例（近地小行星与地球的交会状态）与有关权威性的结果作了比较，证实这些研究结果确实是可信的。在给出的力学模型中，考虑了所有可能影响近地小行星运动的力学因素，包括各大天体和较大的主带小行星的引力作用、有关天体的扁率影响以及源于太阳引力的后牛顿效应。而在计算方法中，合理地处理了变步长问题和月球位置量这种相对而言的快变化问题，使得数值求解一个高维方程组时，对各天体而言，可采用同一步长进行 积分，避免了求解过程中的复杂性。