用正行列式解瓶颈指派问题     

由雷  岳中亮 《广东海洋大学学报》2007,27(6):67-70

用正行列式作为工具，给出了瓶颈指派问题新的解法，并利用正行列式的值求出了瓶颈指派问题的全部最优解。最后通过一个实例说明该算法的实用和有效性。  相似文献   

用正行列式解瓶颈指派问题     

由雷  岳中亮 《广东海洋大学学报》2007,27(6):67-70

用正行列式作为工具,给出了瓶颈指派问题新的解法,并利用正行列式的值求出了瓶颈指派问题的全部最优解。最后通过一个实例说明该算法的实用和有效性。  相似文献   

On the Centre Manifold of Collinear Points in the Planar Three-Body Problem     

Regina Martínez  Anna Samà 《Celestial Mechanics and Dynamical Astronomy》2003,85(4):311-340

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.  相似文献   

The edge wave superposition method (2-D scalar problem)     

K. D. Klem-Musatov  A. M. Aizenberg 《Geophysical Journal International》1989,99(2):351-367

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Fault plane solutions of earthquakes and active tectonics of the Tibetan Plateau and its margins   总被引：18，自引：0，他引：18  

Peter Molnar  Hélène Lyon-Caent 《Geophysical Journal International》1989,99(1):123-154

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The general solution of the HENON–HEILES problem     

K.?E.?PapadakisEmail author  C.?L.?Goudas  G.?A.?Katsiaris 《Astrophysics and Space Science》2005,295(3):375-396

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.  相似文献   

Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem     

A. J. Maciejewski  S. M. Rybicki 《Celestial Mechanics and Dynamical Astronomy》2004,88(3):293-324

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L ₄, L ₅. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date.  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   

Multiple solutions in preliminary orbit determination from three observations     

Giovanni Federico Gronchi 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):301-326

Charlier’s theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace’s method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace’s and Gauss’ methods. We also provide a geometric definition of a curve that generalizes Charlier’s limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier’s: they may change according to the value of a parameter that depends on the observations.  相似文献   

Using micro-catchment experiments for multi-local scale modelling of nature-based solutions     

Barry Hankin  Trevor J. C. Page  Nick A. Chappell  Keith J. Beven  Paul J. Smith  Ann Kretzschmar  Rob Lamb 《水文研究》2021,35(11):e14418

The Q-natural flood management project has co-developed with the Environment Agency 18 monitored micro-catchments (~1 km²) in Cumbria, UK installing calibrated flumes aimed at quantifying the potential shift in observed flows resulting from a range of nature-based-solutions installed by local organizations. The small-scale reduces the influence of variability characterizing larger catchments that would otherwise mask any such shifts, which we attempt to relate to a shift in model parameters. This paper demonstrates an approach to applying donor-parameter-shifts obtained from modelling two of the paired micro-catchments to a much larger scale, in order to understand the potential for improved distributed modelling of nature-based solutions in the form of additional tree-planting. The models include a rainfall-runoff model, Dynamic Topmodel, and a 2D hydrodynamic model, JFlow, permitting analysis of changes in hillslope processes and channel hydrodynamics resulting from a range of distributed measures designed to emulate natural hydrological processes that evaporate, store or infiltrate flows. We report on attempts to detect shift in hydrological response using one of the paired-micro-catchment moorland versus forestry sites in Lorton using Dynamic Topmodel. A donor-parameter-shift approach is used in a hypothetical experiment to represent new woodland in a much larger catchment, although testing all combinations of spatial planting strategies, responses to multiple-extremes, failure-modes and changes to synchronization becomes intractable to support good decision making. We argue that the problem can be re-framed to use donor-parameter-shifts at multi-local-scale catchments above communities known to be at risk, commensurate with most of the evidence of NbS impacts being effective at the small scale (ca. 10 km²). This might lead to more effective modelling to help catchment managers prioritize those communities-at-risk where there is more evidence that NbS might be effective.  相似文献