On Motions Near the Lagrange Equilibrium Point L 4 in the Case of Routh's Critical Mass Ratio     

Boris Bardin 《Celestial Mechanics and Dynamical Astronomy》2002,82(2):163-177

We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L ₄ when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L ₄. We also show that in the case of instability of L ₄ the trajectories starting in a vicinity of L ₄ remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

A complex analytic solution for the attitude motion of a near-symmetric rigid body under body-fixed torques     

P. Tsiotras  J. M. Longuski 《Celestial Mechanics and Dynamical Astronomy》1991,51(3):281-301

Although analytic solutions for the attitude motion of a rigid body are available for several special cases, a comprehensive theory does not exist in the literature for the more complicated problems found in spacecraft dynamics. In the present paper, analytic solutions in complex form are derived for the attitude motion of a near-symmetric rigid body under the influence of constant body-fixed torques. The solution is very compact, which enables efficient and rapid machine computation. Numerical simulations reveal that the solution is very accurate when applied to typical spinning spacecraft problems.  相似文献   

An analytical assessment on the impact of covers on the onset of air convection in mine wastes     

Ning Lu 《国际地质力学数值与分析法杂志》2001,25(4):347-364

If a mine waste pile is left open, an active chemical reaction of oxidation is often found due to the commonly high content of pyritic materials. The oxidation of pyrites is an exothermic process and the released heat will promote the flow of fresh oxygen from the surrounding atmosphere into the waste dump. As a result, oxidation reaction will accelerate and temperature within the dump can increase to as high as 60°C above the ambient temperature. The oxidation process also releases sulphuric acid and hydrogen ions into ground water to cause water contamination. Low‐permeability covers such as clay liners have been recently proposed to abate the oxidation process in mine wastes. The effectiveness of using low‐permeability materials to cover mine wastes in order to suppress the pyrite oxidation is examined. By conducting the theoretical analysis of the onset of convective air flow within waste rocks, the conditions under which soil gas flow is significant are identified. By comparing the results with previous field measurements and theoretical analysis for the uncovered conditions, it is shown that low‐permeability covers can effectively suppress soil gas flow and slow down the pyrite oxidation process in mine wastes. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

一阶可变号非线性奇异初值问题     

杨光崇 《成都信息工程学院学报》2005,20(2):213-218

获得了一类一阶可变号非线性奇异初值问题的新结果。  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   

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