On a global expansion of the disturbing function in the planar elliptic restricted three-body problem

Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities.Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.     

Long-Period Variations of the Eccentricity Vector Valid also for Near Circular Orbits around a Non-Spherical Body

This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity. We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis, inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations or librations around an equilibrium point.     

On the calculation of perturbations in the radial position of satellites

With the aim of analyzing the errors in the radial position of satellites, we give in this paper the expressions for the radial perturbation which include the complete zeroth- and first-order terms in the orbital eccentricity. A simpler and faster method of calculating the perturbation is given.     

关于修改港工钢筋混凝土规范小偏心受压构件正截面强度计算的建议

本文提出在小偏心受压构件正截面强度计算中，取消弯曲抗压强度ｆｃｍ（Ｒｗ），采用轴心抗压强度ｆｃ，这与构件的实际破坏形态相符。对小偏心受压构件正截面强度计算提出了设计建议。特别是对工程上大量应用的矩形截面对称配筋小偏压构件提示了简捷的设计方法，与以往的近似计算方法相比具有物理概念明确，精度高，方法简捷的特点。     

Periodic accumulation and destruction of aeolian erg sequences in the Permian Cedar Mesa Sandstone, White Canyon, southern Utah, USA

The Permian Cedar Mesa Sandstone represents the product of at least 12 separate aeolian erg sequences, each bounded by regionally extensive deflationary supersurfaces. Facies analysis of strata in the White Canyon area of southern Utah indicates that the preserved sequences represent erg‐centre accumulations of mostly dry, though occasionally water table‐influenced aeolian systems. Each sequence records a systematic sedimentary evolution, enabling phases of aeolian sand sea construction, accumulation, deflation and destruction to be discerned and related to a series of underlying controls. Sand sea construction is signalled by a transition from damp sandsheet, ephemeral lake and palaeosol deposition, through a phase of dry sandsheet deposition, to the development of thin, chaotically arranged aeolian dune sets. The onset of the main phase of sand sea accumulation is reflected by an upward transition to larger‐scale, ordered sets which represent the preserved product of climbing trains of sinuous‐crested transverse dunes with original downwind wavelengths of 300–400 m. Regularly spaced reactivation surfaces indicate periodic shifts in wind direction, which probably occurred seasonally. Compound co‐sets of cross strata record the oblique migration of superimposed slipfaced dunes over larger, slipfaceless draa. Each aeolian sequence is capped by a regionally extensive supersurface characterized by abundant calcified rhizoliths and bioturbation and which represents the end product of a widespread deflation episode whereby the accumulation surface was lowered close to the level of the water table as the sand sea was progressively cannibalized by winds that were undersaturated with respect to their potential carrying capacity. Aeolian sequence generation is considered to be directly attributable to cyclical changes in climate and related changes in sea level of probable glacio‐eustatic origin that characterize many Permo‐Carboniferous age successions. Sand sea construction and accumulation occurred during phases of increased aridity and lowered sea level, the main sand supply being former shallow marine shelf sediments that lay to the north‐west. Sand sea deflation and destruction would have commenced at, or shortly after, the time of maximum aridity as the available sand supply became exhausted. Restricted episodes of non‐aeolian accumulation would have occurred during humid (interglacial) phases, accumulation and preservation being enabled by slow rises in the relative water table. Subsidence analysis within the Paradox Basin, together with comparisons to other similar age successions suggests that the climatic cycles responsible for generating the Cedar Mesa erg sequences could be the product of 413 000 years so‐called long eccentricity cycles. By contrast, annual advance cycles within the aeolian dune sets indicate that the sequences themselves could have accumulated in just a few hundred years and therefore imply that the vast majority of time represented by the Cedar Mesa succession was reserved for supersurface development.     

Approximate analysis methods for asymmetric plan base‐isolated buildings

An approximate method for linear analysis of asymmetric‐plan, multistorey buildings is specialized for a single‐storey, base‐isolated structure. To find the mode shapes of the torsionally coupled system, the Rayleigh–Ritz procedure is applied using the torsionally uncoupled modes as Ritz vectors. This approach reduces to analysis of two single‐storey systems, each with vibration properties and eccentricities (labelled ‘effective eccentricities’) similar to corresponding properties of the isolation system or the fixed‐base structure. With certain assumptions, the vibration properties of the coupled system can be expressed explicitly in terms of these single‐storey system properties. Three different methods are developed: the first is a direct application of the Rayleigh–Ritz procedure; the second and third use simplifications for the effective eccentricities, assuming a relatively stiff superstructure. The accuracy of these proposed methods and the rigid structure method in determining responses are assessed for a range of system parameters including eccentricity and structure flexibility. For a subset of systems with equal isolation and structural eccentricities, two of the methods are exact and the third is sufficiently accurate; all three are preferred to the rigid structure method. For systems with zero isolation eccentricity, however, all approximate methods considered are inconsistent and should be applied with caution, only to systems with small structural eccentricities or stiff structures. Copyright © 2001 John Wiley & Sons, Ltd.     

新近纪海相生物地层事件年龄新编

介绍新近纪海相生物地层研究的新进展。2004年新的"国际地质年代表"以405ka偏心率长周期为基础来划分新近纪的主要地层界线,标志着轨道地层学时代的到来。新生代包括E1—E162偏心率长周期,底界的年龄为65.5±0.3Ma,其中新近纪有E1—E58周期,底界年龄为23.03Ma,并且根据天文调谐得出一系列新的古地磁年龄和生物事件年龄。由于这些新年龄,特别是接近新近纪底部的年龄与早期结果相差0.5Ma或更大,所以将其汇总介绍,以求与当前国际研究保持同步衔接,增强海洋新近纪高分辨率地层工作的准确性。     

Contribution of dendrogeomorphology to the dating of secondary processes on dormant rockslides

Rockslides in the Variscan orogenic belt of the Central Europe are a rare and poorly studied phenomenon. These relatively stable features have recently been shaped by secondary rockfall, toppling, sliding, or slumping. On afforested slopes, such processes can be efficiently analysed and dated by dendrogeomorphic methods. We performed detailed analyses of 355 increment cores from 81 Picea abies (L.) Karst. trees growing on two dormant rockslides in northeastern Czechia to reconstruct the activity of rock block movements and rockfalls. For the event determination we used standard event-response (I_t) index and a semi-quantitative approach involving logical spatial position of disturbed trees during a three-year period. Furthermore, climate preparatory and triggering factors were analysed to investigate possible main drivers of recent secondary processes. Overall, four periods of certain block reactivations at the Prudký site since 1940 and seven periods of certain block reactivations at the Rudohorský site since 1834 were reconstructed. Most of the events can be dated to the period 1960–2000, but our data do not indicate any high-magnitude activity. This paper also demonstrates the results of tree eccentric growth not only in the main supposed direction of stem tilting but also in the direction perpendicular to the main direction when ca. 40% of all trees growing on rock blocks recorded the movements in both analysed axes of stem tilting, suggesting possible complex deformation and different directions of block movements over time. It also appeared that the periods with greatest activity of secondary movements were characterised by a significantly higher rain-on-snow factor (p = 0.007 and 0.026 at the Prudký and the Rudohorský site, respectively) thus indicating block detachments during periods of rapid snowmelt.     

Inelastic torsional response of buildings to the 1985 Mexican earthquake: a parametric study

This study aims to determine the influence of torsional coupling on the inelastic response of a series of models representing typical structural configurations in real buildings. The lake bed (SCT) east-west component of the 1985 Mexico City earthquake was employed in the analysis, and is representative of a severe ground motion known to have induced large inelastic structural deformations in a high proportion of those buildings having asymmetrical distributions of stiffness and/or strength. Material non-linearity in lateral load-resisting elements has been defined using a hysteretic Ramberg-Osgood model. Structural eccentricities have been introduced into the building models by (i) asymmetrical distributions of stiffness and/or strength, (ii) asymmetrical configuration of lateral load-resisting elements, or (iii) varying post-elastic material behaviour in the resisting elements. The dynamic inelastic response of these models has been obtained by a numerical integration of the relevant equations of motion, expressed in a non-dimensional incremental form.

In the elastic range, the results correlate well with those of previous studies. In the inelastic range, it is concluded that the peak ductility demand of the worst-affected element increases with the ground excitation level across the range of building periods considered, and that the influence of torsional coupling on the key response parameters is model dependent. Most significantly, the strength eccentricity relative to the centre of mass has been shown to influence the peak edge displacement response more than conventionally employed stiffness eccentricity.     

Solution to the Stokes Boundary-Value Problem on an Ellipsoid of Revolution

We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity e₀ of the ellipsoid of revolution is less than 0·65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the E-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point = 0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function.