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51.
Sandro Da Silva Fernandes 《Celestial Mechanics and Dynamical Astronomy》1994,58(3):297-308
The classic Lagrange's expansion of the solutionE(e, M) of Kepler's equation in powers of eccentricity is extended to highly eccentric orbits, 0.6627 ... <e<1. The solutionE(e, M) is developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of the expansion are given in terms of the derivatives of the Bessel functionsJ
n
(ne). The expansion is convergent for values of the eccentricity such that |e–e*|<(e*), where the radius of convergence (e*) is a positive real number, which is calculated numerically. 相似文献
52.
Makhlouf Amar 《Celestial Mechanics and Dynamical Astronomy》1991,52(4):397-406
We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t). 相似文献
53.
Hydrocyclones are widely used in the mining and chemical industries. An attempt has been made in this study, to develop a CFD (computational fluid dynamics) model, which is capable of predicting the flow patterns inside the hydrocyclone, including accurate prediction of flow split as well as the size of the air-core. The flow velocities and air-core diameters are predicted by DRSM (differential Reynolds stress model) and LES (large eddy simulations) models were compared to experimental results. The predicted water splits and air-core diameter with LES and RSM turbulence models along with VOF (volume of fluid) model for the air phase, through the outlets for various inlet pressures were also analyzed. The LES turbulence model led to an improved turbulence field prediction and thereby to more accurate prediction of pressure and velocity fields. This improvement was distinctive for the axial profile of pressure, indicating that air-core development is principally a transport effect rather than a pressure effect. 相似文献
54.
Ice and snow have often helped physicists understand the world. On the contrary it has taken them a very long time to understand the flow of the glaciers. Naturalists only began to take an interest in glaciers at the beginning of the 19th century during the last phase of glacier advances. When the glacier flow from the upslope direction became obvious, it was then necessary to understand how it flowed. It was only in 1840, the year of the Antarctica ice sheet discovery by Dumont d'Urville, that two books laid the basis for the future field of glaciology: one by Agassiz on the ice age and glaciers, the other one by canon Rendu on glacier theory. During the 19th century, ice flow theories, adopted by most of the leading scientists, were based on melting/refreezing processes. Even though the word ‘fluid’ was first used in 1773 to describe ice, more the 130 years would have to go by before the laws of fluid mechanics were applied to ice. Even now, the parameter of Glen's law, which is used by glaciologists to model ice deformation, can take a very wide range of values, so that no unique ice flow law has yet been defined. To cite this article: F. Rémy, L. Testut, C. R. Geoscience 338 (2006). 相似文献
55.
Khaled S. Balkhair 《Hydrogeology Journal》2006,14(7):1380-1382
56.
57.
58.
泥石流汇流槽可靠度分析 总被引:2,自引:1,他引:2
汇流槽是泥石流治理工程中常用的工程措施之一。文章基于汇流槽的倾倒破坏、滑移破坏及地基破坏模式,通过对汇流槽设计影响强烈的岩土参数、几何特征、荷载因素等敏感因子的求解方法及分布特征分析,从汇流槽的抗倾稳定、抗滑稳定和基底应力要求三方面建立极限状态方程。对于每个极限状态方程,在泰勒级数对非线性极限状态方程线性化后,运用一次二阶矩的理论,先假定失效点P^*,求解出相应的均值和方差。然后根据可靠的定义,得到相应的可靠度指标,通过迭代法求解真正失效点的可靠度指标βi。最后根据3个状态方程相互独立的假定,得出整个结构的可靠度指标β。该方法在平川泥石流防治工程中得到了成功的运用。这对于可靠度设计方法在泥石流防治工程中的运用进行了有益的探讨。 相似文献
59.
EFG法在土体固结中的应用 总被引:4,自引:0,他引:4
EFGM作为一种新的数值计算方法,具有只需节点信息而无段单元的特性,故在解固结方程方面有很大的优势。在计算分析中,此法容易构造固结方程的EFGM刚度矩阵和处理不同边界条件。对单面排水等条件的计算结果表明,EFGM在解决固结变形问题上,精度较高,处理边界准确。 相似文献
60.
为了计算高温,高压和高密度流体的热力学性质,提出了一个具有19个参数的维里型状态方程,其中参数与温度间的函数关系采用由Sutherland位能函数导出的维里系数近似式。除临界点附近以外,在已报道的pVT数据所覆盖的大部分超临界区域内,该方程均可适用。用该方程对H2O,CH4,H2,CO2,CO和O2等流体pVT关系的计算结果令人满意,其中pVT上限分别为:91-610GPa,1.6-11.0cm^3/mol,4000-5000K。计算体积的平均偏 小于0.8%,最大偏差小于5.4%。 相似文献