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This paper studies the relative motion of satellite formation flying in arbitrary elliptical orbits with no perturbation.
The trajectories of the leader and follower satellites are projected onto the celestial sphere. These two projections and
celestial equator intersect each other to form a spherical triangle, in which the vertex angles and arc-distances are used
to describe the relative motion equations. This method is entitled the reference orbital element approach. Here the dimensionless
distance is defined as the ratio of the maximal distance between the leader and follower satellites to the semi-major axis
of the leader satellite. In close formations, this dimensionless distance, as well as some vertex angles and arc-distances
of this spherical triangle, and the orbital element differences are small quantities. A series of order-of-magnitude analyses
about these quantities are conducted. Consequently, the relative motion equations are approximated by expansions truncated
to the second order, i.e. square of the dimensionless distance. In order to study the problem of periodicity of relative motion,
the semi-major axis of the follower is expanded as Taylor series around that of the leader, by regarding relative position
and velocity as small quantities. Using this expansion, it is proved that the periodicity condition derived from Lawden’s
equations is equivalent to the condition that the Taylor series of order one is zero. The first-order relative motion equations,
simplified from the second-order ones, possess the same forms as the periodic solutions of Lawden’s equations. It is presented
that the latter are further first-order approximations to the former; and moreover, compared with the latter more suitable
to research spacecraft rendezvous and docking, the former are more suitable to research relative orbit configurations. The
first-order relative motion equations are expanded as trigonometric series with eccentric anomaly as the angle variable. Except
the terms of order one, the trigonometric series’ amplitudes are geometric series, and corresponding phases are constant both
in the radial and in-track directions. When the trajectory of the in-plane relative motion is similar to an ellipse, a method
to seek this ellipse is presented. The advantage of this method is shown by an example. 相似文献
63.
This work develops a top‐down modelling approach for storm‐event rainfall–runoff model calibration at unmeasured sites in Taiwan. Twenty‐six storm events occurring in seven sub‐catchments in the Kao‐Ping River provided the analytical data set. Regional formulas for three important features of a streamflow hydrograph, i.e. time to peak, peak flow, and total runoff volume, were developed via the characteristics of storm event and catchment using multivariate regression analysis. Validation of the regional formulas demonstrates that they reasonably predict the three features of a streamflow hydrograph at ungauged sites. All of the sub‐catchments in the study area were then adopted as ungauged areas, and the three streamflow hydrograph features were calculated by the regional formulas and substituted into the fuzzy multi‐objective function for rainfall–runoff model calibration. Calibration results show that the proposed approach can effectively simulate the streamflow hydrographs at the ungauged sites. The simulated hydrographs more closely resemble observed hydrographs than hydrographs synthesized using the Soil Conservation Service (SCS) dimensionless unit hydrograph method, a conventional method for hydrograph estimation at ungauged sites in Taiwan. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
64.
A large data set on ripples was collected and examined. A set of new formulas for the prediction of the ripple characteristics is proposed with an emphasis on the disappearance of the ripples. The ripple wavelength was observed to be proportional to the bottom wave excursion but also to be a function of the grain-related Shields parameter and wave period parameter introduced by Mogridge et al. (1994). The ripple steepness was found to be nearly constant for orbital ripples, and with a sharp decrease for suborbital ripples. Two empirical functions are added including the effects of the critical Shields parameters (inception of transport and inception of sheet flow), i.e. giving the boundaries for the ripple existence's domain. The proposed formulas yield better prediction capabilities compared to the previously published formulas, especially when ripples are washed out. The effect of the ripple characteristics on the roughness height and the calculation of the bed shear stress is also discussed. It appeared that the bed shear stress calculation is more sensitive to the empirical coefficient ar introduced in the estimation of the ripple-induced roughness height or to the limits of existence of the ripples than the ripple characteristics themselves. 相似文献
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流速仪法测流最小水深计算公式推导 总被引：3，自引：1，他引：2
在<河流流量测验规范>中,规定了流速仪法测流垂线、流速测点的分布位置和布置测点时的最小水深,[1]也有这方面的刊载,并列举了部分计算公式,但公式考虑不够全面,而且还不符合规范要求.本文依据规范,按流速仪测点布置情况,分析推导出了具体完整的计算公式,并对测点布置方案选择提出了相应的建议. 相似文献
68.
利用Copula函数建立各分区洪水的联合分布,基于联合概率密度最大原则,推导得到最可能地区组成法的计算通式,并用来推求梯级水库下游断面的设计洪水。选择清江流域水布垭-隔河岩-高坝洲梯级水库为例,开展了验证和方法比较研究。结果表明:最可能地区组成法计算得到的设计洪水值位于同频率地区组成法多方案计算结果的区间之内;受清江梯级水库调洪的影响,宜都断面设计洪水的削峰率十分显著,最可能地区组成法推求100年一遇设计洪水的削峰率达到30.2%。该法具有较强的统计基础,组成方案唯一,结果合理可行,为复杂梯级水库设计洪水的计算提供了一种新途径。 相似文献
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