An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem     

J. Hagel 《Celestial Mechanics and Dynamical Astronomy》2009,103(3):251-266

The model of extended Sitnikov Problem contains two equally heavy bodies of mass m moving on two symmetrical orbits w.r.t the centre of gravity. A third body of equal mass m moves along a line z perpendicular to the primaries plane, intersecting it at the centre of gravity. For sufficiently small distance from the primaries plane the third body describes an oscillatory motion around it. The motion of the three bodies is described by a coupled system of second order differential equations for the radial distance of the primaries r and the third mass oscillation z. This problem which is dealt with for zero initial eccentricity of the primaries motion, is generally non integrable and therefore represents an interesting dynamical system for advanced perturbative methods. In the present paper we use an original method of rewriting the coupled system of equations as a function iteration in such a way as to decouple the two equations at any iteration step. The decoupled equations are then solved by classical perturbation methods. A prove of local convergence of the function iteration method is given and the iterations are carried out to order 1 in r and to order 2 in z. For small values of the initial oscillation amplitude of the third mass we obtain results in very good agreement to numerically obtained solutions.  相似文献   

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory     

Gabriel Mititelu 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):327-342

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.  相似文献   

Stream channel erosion in a rapidly urbanizing region of the US–Mexico border: documenting the importance of channel hardpoints with Structure‐from‐Motion photogrammetry          下载免费PDF全文

Kristine T. Taniguchi  Trent W. Biggs  Eddy J. Langendoen  Carlos Castillo  Napoleon Gudino‐Elizondo  Yongping Yuan  Douglas Liden 《地球表面变化过程与地形》2018,43(7):1465-1477

Urbanization can lead to accelerated stream channel erosion, especially in areas experiencing rapid population growth, unregulated urban development on erodible soils, and variable enforcement of environmental regulations. A combination of field surveys and Structure‐from‐Motion (SfM) photogrammetry techniques was used to document spatial patterns in stream channel geometry in a rapidly urbanizing watershed, Los Laureles Canyon (LLCW), in Tijuana, Mexico. Ground‐based SfM photogrammetry was used to map channel dimensions with 1 to 2 cm vertical mean error for four stream reaches (100–300 m long) that were highly variable and difficult to survey with a differential GPS. Regional channel geometry curves for LLCW had statistically larger slopes and intercepts compared with regional curves developed for comparable, undisturbed reference channels. Cross‐sectional areas of channels downstream of hardpoints, such as concrete reaches or culverts, were up to 64 times greater than reference channels, with enlargement persisting, in some cases, up to 230 m downstream. Percentage impervious cover was not a good predictor of channel enlargement. Proximity to upstream hardpoint, and lack of riparian and bank vegetation paired with highly erodible bed and bank materials may account for the instability of the highly enlarged and unstable cross‐sections. Channel erosion due to urbanization accounts for approximately 25–40% of the total sediment budget for the watershed, and channel erosion downstream of hardpoints accounts for one‐third of all channel erosion. Channels downstream of hardpoints should be stabilized to prevent increased inputs of sediment to the Tijuana Estuary and local hazards near the structures, especially in areas with urban settlements near the stream channel. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

Digital mapping of coastal boulders – high-resolution data acquisition to infer past and recent transport dynamics     

Fabian Boesl  Max Engel  Rodrigo C. Eco  JaN B. Galang  Lia A. Gonzalo  Francesca Llanes  Eva Quix  Helmut Brückner 《Sedimentology》2020,67(3):1393-1410

Coastal boulder fields provide clues to long-term frequency-magnitude patterns of coastal flooding events and have the potential to play an important role in coastal hazard assessment. Mapping boulders in the field is time and labour-intensive, and work on intertidal reef platforms, as in the present study, is physically challenging. By addressing coastal scientists who are not specialists in remote sensing, this contribution reports on the possibilities and limitations of digital applications in boulder mapping in Eastern Samar, Philippines, where recent supertyphoons Haiyan and Hagupit induced high waves, coastal flooding and boulder transport. It is demonstrated how satellite imagery of sub-metre resolution (from Pléiades and WorldView-3 imagery) enables efficient analysis of transport vectors and distances of larger boulders, reflecting variation in latitudes of both typhoon tracks and approaching angles of typhoon-generated waves. During the investigated events, boulders with a-axes of up to 8 m were clearly identified to have been shifted for up to 32 m, mostly along the seaward margin of the boulder field. It is, however, hard to keep track of smaller boulders, and the length of a-axes and b-axes including their orientation is often impossible to map with sufficient accuracy. Orthophotographs and digital surface models created through the application of an unmanned aerial vehicle and the ‘Structure from Motion’ technique provide ultra-high-resolution data, and have the potential to not only improve the results of satellite image analysis, but also those from field mapping and may significantly reduce overall time in the field. Orthophotographs permit unequivocal mapping of a-axes and b-axes including their orientation, while precise values for c-axes can be derived from the respective digital surface models. Volume of boulders is best inferred from boulder-specific Structure from Motion-based three-dimensional models. Battery power, flight speed and altitude determine the limits of the area covered, while patches shielded by the boulders are difficult to resolve. For some tasks, field mapping remains mandatory and cannot be replaced by currently available remote sensing tools: for example, sampling for rock type, density and age dating, recording of lithological separation of boulders from the underlying geological unit and of geomorphic features on a millimetre to decimetre-scale, or documentation of fine-grained sediment transport in between the boulders in supratidal settings. In terms of future events, the digital products presented here will provide a valuable reference to track boulder transport on a centimetre to decimetre-scale and to better understand the hydrodynamics of extreme-wave events on a fringing reef coastline.  相似文献   

Reconstructing historic Glacial Lake Outburst Floods through numerical modelling and geomorphological assessment: Extreme events in the Himalaya          下载免费PDF全文

Matthew J. Westoby  Neil F. Glasser  Michael J. Hambrey  James Brasington  John M. Reynolds  Mohamed A. A. M. Hassan 《地球表面变化过程与地形》2014,39(12):1675-1692

Recession of high‐mountain glaciers in response to climatic change frequently results in the development of moraine‐dammed glacial lakes. Moraine dam failure is often accompanied by the release of large volumes of water and sediment, termed a Glacial Lake Outburst Flood (GLOF). Chukhung Glacier is a small (~3 km²) receding valley glacier in Mt. Everest (Sagarmatha) National Park, Nepal. Unlike many Himalayan glaciers, which possess a thick mantle of supraglacial debris, its surface is relatively clean. The glacier terminus has receded 1.3 km from its maximum Holocene position, and in doing so provided the space for an ice‐contact moraine‐dammed lake to develop. The lake had a maximum volume of 5.5 × 10⁵ m³ and drained as a result of breaching of the terminal moraine. An estimated 1.3 × 10⁵ m³ of material was removed from the terminal moraine during breach development. Numerical dam‐breach modelling, implemented within a Generalised Likelihood Uncertainty Estimation (GLUE) framework, was used to investigate a range of moraine‐dam failure scenarios. Reconstructed outflow peak discharges, including failure via overtopping and piping mechanisms, are in the range 146–2200 m³ s^‐1. Results from two‐dimensional hydrodynamic GLOF modelling indicate that maximum local flow depths may have exceeded 9 m, with maximum flow velocities exceeding 20 m s^‐1 within 700 m of the breach. The floodwaters mobilised a significant amount of material, sourced mostly from the expanding breach, forming a 300 m long and 100 m wide debris fan originating at the breach exit. moraine‐dam. These results also suggest that inundation of the entire floodplain may have been achieved within ten minutes of initial breach development, suggesting that debris fan development was rapid. We discuss the key glaciological and geomorphological factors that have determined the evolution of a hazardous moraine‐dammed lake complex and the subsequent generation of a GLOF and its geomorphological impact. © 2014 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.  相似文献   

Assessing the performance of structure‐from‐motion photogrammetry and terrestrial LiDAR for reconstructing soil surface microtopography of naturally vegetated plots          下载免费PDF全文

Sayjro Kossi Nouwakpo  Mark A. Weltz  Kenneth McGwire 《地球表面变化过程与地形》2016,41(3):308-322

Soil microtopography is a property of critical importance in many earth surface processes but is often difficult to quantify. Advances in computer vision technologies have made image‐based three‐dimensional (3D) reconstruction or Structure‐from‐Motion (SfM) available to many scientists as a low cost alternative to laser‐based systems such as terrestrial laser scanning (TLS). While the performance of SfM at acquiring soil surface microtopography has been extensively compared to that of TLS on bare surfaces, little is known about the impact of vegetation on reconstruction performance. This article evaluates the performance of SfM and TLS technologies at reconstructing soil microtopography on 6 m × 2 m erosion plots with vegetation cover ranging from 0% to 77%. Results show that soil surface occlusion by vegetation was more pronounced with TLS compared to SfM, a consequence of the single viewpoint laser scanning strategy adopted in this study. On the bare soil surface, elevation values estimated with SfM were within 5 mm of those from TLS although long distance deformations were observed with the former technology. As vegetation cover increased, agreement between SfM and TLS slightly degraded but was significantly affected beyond 53% of ground cover. Detailed semivariogram analysis on meter‐square‐scale surface patches showed that TLS and SfM surfaces were very similar even on highly vegetated plots but with fine scale details and the dynamic elevation range smoothed out with SfM. Errors in the TLS data were mainly caused by the distance measurement function of the instrument especially at the fringe of occlusion regions where the laser beam intersected foreground and background features simultaneously. From this study, we conclude that a realistic approach to digitizing soil surface microtopography in field conditions can be implemented by combining strengths of the image‐based method (simplicity and effectiveness at reconstructing soil surface under sparse vegetation) with the high accuracy of TLS‐like technologies. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

Hydrodynamics and Thermodynamics of Newtonian Stars     

Ho-Young Kwak  Jung-Hwan Jun 《地球物理与天体物理流体动力学》2013,107(1):45-58

We investigated spherically symmetric solution for nonrelativistic cosmological fluid equations and thermodynamic equation of state for Newtonian stars. It was shown that the assumption of a polytropic equation, , at the center of the star only suffices to integrate the equations explicitly. Our exact solution yields many fruitful results such as stellar stability, spherical oscillation and collapses of stars. Pressure, temperature, and density profiles inside stars were obtained. Central densities, pressures and temperatures of the Newtonian stars such as Sun, Jupiter and Saturn were also calculated. Collapse and expansion mechanism was explained by the heat transfer mechanism inside star. The upper bound value of white dwarf mass obtained by the Newtonian cosmological fluid equations turns out to be comparable to the static limit of Chandrasekhar one. Motion of the Universe was also discussed within the framework of Newtonian mechanics. Our calculation results without considering nuclear reactions inside stars may be applicable to the formation of protostars.  相似文献   

基于震动台试验的数字强震动仪一致性研究     

卢大伟  周雍年  王玉石  连尉平 《世界地震工程》2008,24(4)

中国数字强震动台网作为"十五"重大项目中国数字地震观测网络的重要组成部分之一,是迄今为止我国投资最多、规模最大的强震动观测台网。由于台网采用了多种数字强震动仪,不同型号数字强震动仪的一致性程度直接影响到台网的观测质量。通过对台网所用5种数字强震动仪的振动台试验和结果分析,表明这5种数字强震动仪的一致性良好,能够满足中国数字强震动台网建设要求。  相似文献   

多尺度相关性分析的机载双极化InSAR轨道误差校正方法     

何永红  靳鹏伟  蒋陈纯 《地球信息科学学报》2021,23(4):670-679

在高分辨率机载干涉SAR成像处理过程中,由于载机飞行过程中偏离理想轨迹,需要高精度的惯导系统和GPS系统记录载机的运动轨迹并进行运动补偿.然而,由于目前传感器导航精度的限制,在完成运动补偿处理后仍然存在轨道误差,从而影响干涉相位的精度,本文提出了一种机载双极化InSAR轨道误差去除方法.该方法利用小波多尺度分析对不同极...  相似文献   

A new approach for measuring surface hydrological connectivity     

Joshua M. Wolstenholme  Mark W. Smith  Andy J. Baird  Thomas G. Sim 《水文研究》2020,34(3):538-552

The development of surface hydrological connectivity is a key determinant of flood magnitude in drylands. Thresholds in runoff response may be reached when isolated runoff-generating areas connect with each other to form continuous links to river channels, enabling these areas to contribute to flood hydrographs. Such threshold behaviour explains observed nonlinearities and scale dependencies of dryland rainfall–runoff relationships and complicates attempts at flood prediction. However, field methods for measuring the propensity of a surface to transmit water downslope are lacking, and conventional techniques of infiltration measurement are often inappropriate for use on non-agricultural drylands. Here, we argue for a reconceptualization of the dryland surface runoff process, suggesting that the downslope transfer of water should be considered alongside surface infiltration; that is, there is a need for the “aggregated” measurement of infiltration and overland flow hydraulics. Surface application of a set volume of water at a standardized rate generates runoff that travels downslope; the distance it travels downslope is determined by infiltration along the flow, integration of flow paths, and flow resistance. We demonstrate the potential of such a combined measurement system coupled with structure-from-motion photogrammetry to identify surface controls on runoff generation and transfer on dryland hillslopes, with vegetation, slope, surface stone cover, and surface roughness all having a significant effect. The measurement system has been used on slopes up to 37° compared with the flat surface typically required for infiltration methods. On average, the field workflow takes ~10–15 min, considerably quicker than rainfall simulation. A wider variety of surfaces can be sampled with relative ease, as the method is not restricted to stone and vegetation-free land. We argue that this aggregated measurement represents surface connectivity and dryland runoff response better than standard hydrological approaches and can be applied on a much greater variety of dryland surfaces.  相似文献