On the rotational motion of deformable celestial bodies

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Moments of the lunar disturbing force

Summary The components of the moments of the external force due to the gravitational effect of the Moon are derived, which causes disturbances in the motion of the Earth round its mass centre, taking into account the gravitational fields of both bodies in the form of a development in terms of harmonics upto degree n=4. This paper ties up with [3–5] and the notations are identical.     

天体运行的介质层壳与离散轨道引论

采用介质层壳弯曲的唯象方法,在规整三维空间中给出了能量曲率方程及物体间的能量引力形式表述,其引力方程的二个条件解分别与Newton引力理论及Einstein引力理论的有关结果相近．讨论了目前分维微积分在函数方面的局限性,给出了相似扩展方程,随后通过讨论天体运行轨道的基线扩展特征,给出了天体运行的离散轨道方程,并以太阳系行星及部分卫星为例,给出了这些天体运行离散轨道方程的具体表述形式。     

天体运行轨道的一般性Binet方程形式

通过讨论已有质速关系的方程形式,给出质速关系的等效极坐标方程及其Binet方程,进而给出质速关系及质能关系的几个较为具体的方程形式,包括超光速运动形式.随后应用质能关系探讨介质层壳弯曲方法中能量曲率方程解的一般形式,给出天体运行轨道的一般性Binet方程,给出了行星近日点进动、光线弯曲的解析分析.     

Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies

Satellite orbits have been routinely used to produce models of the Earth’s gravity field. In connection with such productions, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this note, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, setting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies. Supported by a Grant-in-Aid for Scientific Research (Grant No. B19340129)     

On the rotational components of seismic motion

The surface motion during an earthquake is different from point to point depending on the propagation properties of the seismic waves. Rocking and torsion are thus present in the free field, in proportion to the spatial derivatives of the surface motion with respect to a given direction. These derivatives are inversely proportional to the apparent wave velocity in that direction, so the smaller the wave apparent velocity, the more important its contribution to the rotations. In this respect, a marked contribution to surface rotations from surface waves is expected. A mathematical model is presented, based on a detailed representation of soil impedance, an approximate identification of surface waves and a deconvolution of body waves in P and SV contributions. Through this model the surface motion obtained from the records of strong-motion accelerometers can be expressed as a superposition of plane waves of known wavelengths. Rocking response spectra are computed and results are compared with previously published spectra. A sensitivity analysis is performed on some parameters of the model.     

小天体探测任务及形状建模综述

小天体形状建模对小天体探测具有重要的工程和科学意义.精细的地形模型是进行小天体着陆和采样返回的前提条件,同样也是进行小天体形貌分析和地质特征及成因探讨的基础数据.本文首先回顾了过去十几年中主要的小天体探测任务,对其相关的小天体三维表面模型重建工作进行介绍,在此基础上对主流的重建方法进行总结、分析,讨论了各种方法的局限性...     

对地磁发电机理论的反思与天体磁场研究展望

由地球磁场的基本特征和电磁场理论,证明了流体外核不可能产生偶极磁场,地磁发电机理论对偶极磁场是无效的.并对地球和天体磁场的研究方向和方法进行了展望:偶极场与核心部分的自组织结构有关,多极子场与外部各层的组织结构或运动状态有关.     

Impulsive Dirac‐delta forces in the rocking motion

In this work the classical theory of one block rocking motion is revisited. A Dirac‐delta type interaction as impact mechanism is found to be an alternative for the traditional model. Numerical computations with this new formulation have shown that the agreement with the classical theory is excellent for the case of slender blocks and small displacements. Good agreement with experimental data has also been found for the case of arbitrary angles and slenderness. The approach presented in this paper opens new lines for further theoretical developments and computational applications. Copyright © 2004 John Wiley & Sons, Ltd.     

Timing of rotational motion of Southwest Japan inferred from paleomagnetism

Paleomagnetic field directions for the period younger than 35 Ma are obtained from igneous rocks distributed in the San'in district, Inner Zone of Southwest Japan. The remanent magnetization of samples between 30 and 35 Ma old are fairly well grouped with a mean direction of D = 65.9°, I = 48.6°, and ₉₅ = 6.5°. This result establishes that Southwest Japan rotated clockwise 56 ± 12° during the past 30 m.y. A declination value of about 60° is observed in the rocks of 28 Ma ( D = 52.2°, I = 33.5°) and 21 Ma (D = 69.9°, I = 49.5°). Comparing this with results from dacitic rocks with an age of 15 Ma in other areas of Southwest Japan suggests that rotational motion did not occur possibly until 15 Ma. These results require that the rotation of Southwest Japan occurred just after the Shikoku Basin had been created.     

Time-frequency response spectrum of rotational ground motion and its application

The rotational seismic motions are estimated from one station records of the 1999 Jiji (Chi-Chi), Taiwan, earthquake based on the theory of elastic plane wave propagation. The time-frequency response spectrum (TFRS) of the rota-tional motions is calculated and its characteristics are analyzed, then the TFRS is applied to analyze the damage mechanism of one twelve-storey frame concrete structure. The results show that one of the ground motion components can not reflect the characteristics of the seismic moti...     

On the characteristics of ground motion rotational components using Chiba dense array data

An effort is made to examine the properties of rotational (torsional and rocking) ground motions using Chiba dense array data. The Chiba array system, located 30 km east of Tokyo, Japan, is composed of 15 boreholes with separation distances varying from 5 to 320 m. This provides a unique opportunity to examine the characteristics of rotational components. For this purpose, 17 events are considered and rotational ground motions are evaluated using spatial derivatives of translational ones. The effects of seismological parameters and separation distances between stations on properties of rotational motions are examined, showing a sudden increase in rotational motions for the earthquakes with large magnitude or PGA and decrease of these motions with increasing separation distance. While the duration of torsional motion is found to be larger than translational ones, there is no significant difference between durations of rocking and vertical motions. The effects of separation distance and earthquake magnitude on rotational response spectra are also investigated. The normalized rotational response spectra are found to be strongly affected by separation distance. The spectral ratios of rotational and translational motions are not linearly proportional to period as suggested by the previous studies. Finally, the torsional motion is predicted from translation ones for different separation distances at the site. The comparison of the predicted and the calculated torsional motions reveals a weak estimation in close separation distances (<30m) and satisfactory predictions in other cases. Copyright © 2007 John Wiley & Sons, Ltd.     

On a certain doubt L. Euler had with respect to determining the rotation of the earth and of celestial bodies

Summary The application of Euler's postulate , which determines rotation (here denotes the derivative of the angular momentum with respect to time, L the resultant torque of exterior forces relative to the centre of inertia), to a celestial body, which is not spherically symmetric, had aroused doubts in Euler himself because of the displacement of the resultant attractive force of other celestial bodies from the said centre. As Minding had noted, it is more logical to compute the resultant torque relative to a point at which the torque has a minimum. This point should be named the attrahentis centrum after Euler. Newton was aware of this displacement of the resultant force and had mentioned it in the Principia. A review of Euler's works connected with this subject is given.     

Examining ambient noise using colocated measurements of rotational and translational motion

In the past decade, a number of studies have reported the observation of rotational motion associated with seismic events. We report a first observation of rotational motion in the microseismic ambient noise band. A striking feature of rotational motion measurements is that the information about the seismic phase velocity and source back azimuth is contained in the amplitude ratio of a point measurement of rotation rate and transverse acceleration. We investigate the possibility of applying this method to ambient noise measured with a ring laser and a broadband seismometer at the Wettzell Geodetic Observatory in Germany. Using data in the secondary microseismic band, we recover local phase velocities as well as the back azimuth of the strongest noise source for two different time periods. In order to confirm these findings, we additionally compare the results with classical array processing techniques of the Gr?fenberg array located nearby.     

Adaptation of the S-5-S pendulum seismometer for measurement of rotational ground motion

The Russian electrodynamic seismometer model S-5-S has been adapted for the measurement of rotational ground motion. The mechanical system of the original S-5-S seismometer consists of electrodynamic sensing and damping transducer coils mounted on an asymmetrical double-arm pendulum. This pendulum is suspended on a footing using two pairs of crossed flat springs, which operate as the axis of rotation. The pendulum is stabilised by an additional spring. The S-5-S can be used either as a vertical or as a horizontal sensor. The adaptation of the S-5-S seismometer described below involves removal of the additional spring and installation of an additional mass on the damping arm. Strain gauge angle sensors are installed on one pair of the crossed flat springs. The main dynamic parameters of the rotational seismometer created in this way, i.e. the natural period and damping, are controlled electronically by feedback currents proportional to the angular displacement and angular velocity, both fed to the damping transducer coil. This new seismometer, named the S-5-SR, enables measurement of the rotational component of ground motion around the horizontal or the vertical axes. The output signal from this S-5-SR seismometer can be proportional either to rotational displacement or rotational velocity.     

Criteria for initiation of motion of rigid bodies to base excitation

It is known that when an unanchored rigid body is placed on a horizontal base which oscillates horizontally, it may undergo one of four modes of motion: rest, slide, slide–rock and rock. Initiation of a rigid body into these modes depends on the slenderness ratio of the body, the coefficient of friction between the body and the base and the acceleration of the base. In this study, the coefficient of friction and the base acceleration are considered random. For specific probability distributions of the coefficient of friction and the peak base acceleration, and for various values of the mean and standard deviation of the two random variables, the probabilities of occurrence of these modes of motion are obtained for a body of given slenderness ratio. It is shown that randomness of the coefficient of friction and base peak acceleration should not be ignored. Copyright © 2005 John Wiley & Sons, Ltd.     

机房干扰源的分析

从理论上分析了机房中干扰产生的原因,提出了压低干扰的措施。     

Extracting rotational components of earthquake ground motion using data recorded at multiple stations

Rotational components of earthquake ground motion have not been considered for seismic analysis, design and performance assessment because recordings of these components are unavailable. A number of procedures have been proposed to extract rotational components of ground motion from translational time series recorded at multiple, closely spaced recording stations. In this paper, a new procedure that is capable of capturing higher frequency content in rotational time‐series is presented. The frequencies at which numerical errors are introduced in the solution, which are a function of apparent wave velocity and array dimension, are identified. Results are presented for the proposed procedure, the widely accepted geodetic method, and a single‐station procedure developed by the authors, all using data recorded at the Lotung array in Taiwan. Copyright © 2012 John Wiley & Sons, Ltd.     

天体运行轨道的背景介质理论导引与自相似分形测度计算的分维微积分基础

通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设,介绍了天体运行轨道的具体方程形式及理论框架概要;进一步地通过讨论天体运行轨道Binet方程的一般形式及其行星近日点进动角的解,给出了连续轨道理论与Newton理论及Einstein广义相对论的联系与区别;通过讨论天体运行轨道的分维扩展方程,给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道（稳定性轨道）方程及其预言数据.特别地,作为对天体在较为广泛区域作用曲线的初步探讨推论,指出仅由天体引力难以形成质量密度趋于无穷大的理想黑洞.通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设,进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式,给出分维导数与分数阶导数的区别,随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式,给出了其与目前Hausdorff测度方法（覆盖方法）的区别,并对包括三分Cantor集合、Koch曲线、Sierpinski垫片及正交十字星形等自相似分形在内的测度进行了计算分析.     

Methods for estimating rotational components of seismic ground motion and their numerical comparisons*

Rotational components play an important role in natural earthquake research, engineering seismic investigation, building monitoring, seismic exploration and other fields. Traditional researches mainly focus on three translational components, but less on rotational ones. As the precision of rotational sensing techniques has increased, many scholars have paid more attention to the seismic rotational motions. Because the rotational observations are not very popular before and now, approximately converting the translational components into rotational components is utilized in rotation analysis. Based on numerical six-component seismic data with the finite difference method, we compare three different conversion methods, the travelling-wave, frequency-domain and the difference method, to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.