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Using alternative independent variables in lieu of time has important advantages when propagating the partial derivatives of the trajectory. This paper focuses on spacecraft relative motion, but the concepts presented here can be extended to any problem involving the variational equations of orbital motion. A usual approach for modeling the relative dynamics is to evaluate how the reference orbit changes when modifying the initial conditions slightly. But when the time is a mere dependent variable, changes in the initial conditions will result in changes in time as well: a time delay between the reference and the neighbor solution will appear. The theory of asynchronous relative motion shows how the time delay can be corrected to recover the physical sense of the solution and, more importantly, how this correction can be used to improve significantly the accuracy of the linear solutions to relative motion found in the literature. As an example, an improved version of the Clohessy-Wiltshire (CW) solution is presented explicitly. The correcting terms are extremely compact, and the solution proves more accurate than the second and even third order CW equations for long propagations. The application to the elliptic case is also discussed. The theory is not restricted to Keplerian orbits, as it holds under any perturbation. To prove this statement, two examples of realistic trajectories are presented: a pair of spacecraft orbiting the Earth and perturbed by a realistic force model; and two probes describing a quasi-periodic orbit in the Jupiter-Europa system subject to third-body perturbations. The numerical examples show that the new theory yields reductions in the propagation error of several orders of magnitude, both in position and velocity, when compared to the linear approach. 相似文献
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将多元校正分析法应用于配位滴定中,以EDTA为滴定剂,玻璃电极为指示电极,饱和甘汞电极为参比电极。依据电位滴定原理,对混合三组分:Cu ̄(2+)、Cd ̄(2+)、Zn ̄(2+)、及Cu ̄(2+)、CO ̄(2+)、Ni ̄(2+)进行测定,各金属离子之间的△logK在0.04~2.34之间,计算误差一般小于土10%。 相似文献
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DONG Shuwen Chinese Academy of Geological Sciences Baiwanzhuang Ro Beijing WU Hongling LIU Xiaochun XUE Huaimin Institute of Geomechanics Chinese Academy of Geological Sciences Beijing Fei Zhenbi 《《地质学报》英文版》2002,76(1):69-80
Up to now it is known that almost all ultrahigh-pressure (UHP) metamorphism of non-impact origin occurred in continent-continent collisional orogenic belt, as has been evidenced by many outcrops in the eastern hemisphere. UHP metamorphic rocks are represented by coesite- and diamond-bearing eclogites and eclogite facies metamorphic rocks formed at 650-800℃ and 2.6-3.5 GPa, and most of the protoliths of UHP rocks are volcanic-sedimentary sequences of continental crust. From these it may be deduced that deep subduction of continental crust may have occurred. However, UHP rocks are exposed on the surface or occur near the surface now, which implies that they have been exhumed from great depths. The mechanism of deep subduction of continental crust and subsequent exhumation has been a hot topic of the research on continental dynamics, but there are divergent views. The focus of the dispute is how deep continental crust is subducted so that UHP rocks can be formed and what mechanism causes it to be subducte 相似文献
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Early Carboniferous Radiolarian Fauna from Heiyingshan South of the Tianshan Mountains and Its Geotectonic Significance 总被引:5,自引:0,他引:5
LIU YuInstitute of Geology Chinese Academy of Geological Sciences Baiwanzhuang Ro Beijing 《《地质学报》英文版》2001,75(1):101-108
Abundant and well-preserved fossil radiolarians found from the Artencasher Formation, Heiyingshan of Baicheng County, Xinjiang Uygur Autonomous Region, are identified, including 15 species and 2 unnamed species in 9 genera. The fauna is dominated by the Family Entactiniidae of Spumellaria. According to the faunal characteristics, the radiolarians may be divided into five assemblages, namely, the Triaenosphaera sicarius, Entatinosphaera palimbola, Entactinia vulgaris, Belowea cf. variabilis and Archocyrtium sp assemblages. The fauna may be correlated with that from the Early Carboniferous of Frankenwald and Rein in Germany. Thus, ophiolite was formed in the Carboniferous, while the age of collision between the Ili plate and the Tarim plate is Early Carboniferous. 相似文献
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A Titanosaurian Sauropod Dinosaur with Opisthocoelous Caudal Vertebrae from the Early Late Cretaceous of Liaoning Province, China 总被引:4,自引:0,他引:4
Matthew C. LAMANNA 《《地质学报》英文版》2004,78(4):907-911
We describe a new titanosaurian sauropod dinosaur, Borealosaurus wimani gen. et sp. nov., based on a distinctive mid-distal caudal vertebra from the early Late Cretaceous Sunjiawan Formation exposed in the Shuangmiao village of Beipiao in Liaoning, China. We provisionally refer an isolated tooth crown, a middle caudal vertebra, and a right humerus from the same locality and horizon to this taxon. Borealosaurus is distinguished from other sauropods in its possession of opisthocoelous mid-distal caudal vertebrae. The occurrence of opisthocoelous caudals in Borealosaurus and the Mongolian sauropod Opisthocoelicaudia raises the possibility that these taxa pertain to an as-yet unrecognized titanosaurian subclade endemic to the Cretaceous Asia. 相似文献
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A Simple Monte Carlo Method for Locating the Three-dimensional Critical Slip Surface of a Slope 总被引:2,自引:0,他引:2
XIE Mowen Institute of Environmental Systems Kyushu University Hakozaki -- Higashi Ku Fukuok Japan College of Resource Engineering the University of Science Technology Beijing Xueyuan Ro Haidian District Beijing China 《《地质学报》英文版》2004,78(6):1258-1266
Based on the assumption of the plain-strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope-stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column-based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher. 相似文献
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