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651.
V.S. Kalantonis E.A. Perdios A.E. Perdiou O. Ragos M.N. Vrahatis 《Astrophysics and Space Science》2003,288(4):479-488
The techniques used for the numerical computation of families of periodic orbits of dynamical systems rely on predictor-corrector
algorithms. These algorithms usually depend on the solution of systems of approximate equations constructed from the periodicity
conditions of these orbits. In this contribution we transform the root finding procedure to an optimization one which is applied
on an objective function based on the exact periodicity conditions. Thus, the determination of periodic solutions and families
of such orbits can be accomplished through unconstrained optimization. In this paper we apply and compare some well-known
minimization methods for the solution of this problem. The obtained results are promising.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
652.
E. A. Perdios V. S. Kalantonis M. N. Vrahatis 《Celestial Mechanics and Dynamical Astronomy》2002,84(3):231-244
We present an improved method for locating periodic orbits of a dynamical system of arbitrary dimension. The method first employs the characteristic bisection method (CBM) to roughly locate a periodic orbit, followed by the quadratically convergent Newton method to rapidly refine its position. The method is applied to the physically interesting example of the two degrees of freedom photogravitational problem, and shown to surpass the CBM algorithm and Newton's method alone. 相似文献
653.
S. M. El-Shaboury 《Celestial Mechanics and Dynamical Astronomy》1990,50(3):199-208
The restricted problem of 2 + 2 homogenous axisymmetric ellipsoids such that their equatorial planes coincide with the orbital plane of the centers of mass is considered. The equilibrium solutions of this problem are shown to exist. Six of these solutions are located about the collinear points of the restricted problem of three axisymmetric ellipsoids. A special case of this problem is studied and sixteen solutions are found in the neighborhood of the triangular Lagrangian points. 相似文献
654.
This paper presents the procedure of a computational scheme leading to approximate general solution of the axi-symmetric,2-degrees
of freedom dynamical systems. Also the results of application of this scheme in two such systems of the non-linear double
oscillator with third and fifth order potentials in position variables. Their approximate general solution is constructed
by computing a dense set of families of periodic solutions and their presentation is made through plots of initial conditions.
The accuracy of the approximate general solution is defined by two error parameters, one giving a measure of the accuracy
of the integration and calculation of periodic solutions procedure, and the second the density in the initial conditions space
of the periodic solutions calculated. Due to the need to compute families of periodic solutions of large periods the numerical
integrations were carried out using the eighth order, variable step, R-K algorithm, which secured for almost all results presented
here conservation of the energy constant between 10-9 and 10-12 for single runs of any and all solutions. The accuracy of the approximate general solution is controlled by increasing the
number of family curves and also by `zooming' into parts of the space of initial conditions. All families of periodic solutions
were checked for their stability. The computation of such families within areas of `deterministic chaos' did not encounter
any difficulty other than poorer precision. Furthermore, on the basis of the stability study of the computed families, the
boundaries of areas of `order' and `chaos' were approximately defined. On the basis of these results it is concluded that
investigations in thePoincaré sections have to disclose 3 distinct types of areas of `order' and 2 distinct types of areas
of `chaos'. Verification of the `order'/`chaos' boundary calculation was made by working out several Poincaré surfaces of
sections.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
655.
I. Gacka 《Astrophysics and Space Science》2003,284(3):1069-1085
The present paper demonstrates the results of the numerical integration of equations of motion of a infinitesimal mass pleased
in the neighborhood of the triangular point of the Sun-planet system. There are presented the results for the outer solar
system, i.e. for Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. The long-periodic solutions were searched for the distance
from the Lagrangian point changing from ±0.01 to ±0.10 in canonical units. The Trojans of those planets have the circle, tadpole,
horseshoe and irregular shape of their orbits. Same of those test particles showed a close approach to planet. Other of those
collided with planet and then was removed from the solar system. The tadpole, circle and same trajectories surveyed integration
for 100,000 years.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
656.
For the 1+2 and 2+2 problems, we obtain the equilibrium points, their stability, and the topology of the constant energy manifold. 相似文献
657.
Navin Chandra 《Planetary and Space Science》2004,52(8):747-760
The non-linear stability of the triangular libration point L4 of the restricted three-body problem is studied under the presence of third- and fourth-order resonances, when the more massive primary is a triaxial rigid body and source of radiation. In this study, Markeev's theorems are applied with the help of Moser's theorem. It is found that the stability of the triangular libration point is unstable in the third-order resonance case and in the fourth-order resonance case, this is stable or unstable depending on A1 and A2, and a source of radiation parameter α, where A1, A2 depend upon the lengths of the semi-axes of the triaxial rigid body. 相似文献
658.
The galactic dynamical system expressed by a third-order axisymmetric polynomial potential is investigated numerically by computing periodic solutions. We define as Sthe compact set of initial conditions generating bounded motions, and as S p , with S p ? S, the countable set of all initial conditions generating periodic solutions. Then, we consider the subsets S s p and S a p of S p , where S s p ∪ S a p = S p , S s p S a p = Ø, the first of which corresponds to symmetric periodic solutions, and the second to asymmetric solutions. Then, we approximate the set S s p , leaving treatment of the set S a p of asymmetric solutions for a future publication. The set S s p is known to be dense in S (‘Last Geometric Theorem of Poincar;’, Birkhoff, 1913). Using a computer programme capable to locate all elements of the set S s p that generate symmetric periodic solutions that re-enter after intersecting the axis of symmetry from 1 to ntimes. The results of the approximation of S s p in the total domain and in the sample sub-domains of zooming, we present in graphical form as family curves in the (x, C) plane. The solutions located with the largest periods re-enter after 440 galaxy revolutions while the families calculated fully (initial conditions, period, energy, stability co-efficient) include solutions that re-enter after 340 galaxy revolutions. To advance further the approximation of the set S s p thus obtained, we applied the same procedure inside eight sub-domains of the domain Sinto which we ‘zoomed’ through selection of finer search steps and double maximum periods. The family curves thus calculated presented in the (x, C) plane do not intersect anywhere in some sub-domains and their pattern resembles that of laminar flow. In other sub-domains, however, we found family curves from which branching families emanate. The concepts of completeand non-completeapproximation of S s p in sub-domains of laminar and sub-domains with branching family curves, respectively, is introduced. Also, the concept of basic family of order1, 2, ..., n, are defined. The morphology of individual periodic solutions of all families is investigated, and the types of envelopes found are described. The approximate set S s p was also checked by computing Poincar; sections for energy values corresponding to the mean energy range of the eight sub-domains of zooming mentioned above. These sections show that most parts of the compact domain in Sgenerating non-periodic but bounded solutions correspond to with well-shaped tori that intersect the x-axis, a fact that implies that dominant to exclusive type of periodic solutions are the symmetric ones with two normal crossings of this axis. The presence of non-symmetric periodic solutions as well as of chaotic regions is encountered. All calculations reported here were performed using the variable step R-K 8th-order direct integration and setting the allowable energy variation Δ C= |C start? C end| < 10?13. The output, consisting of many thousands of families and their properties (initial conditions, morphology, stability, etc.), is stored in a directory entitled ‘Atlas of the Symmetric Periodic Solution of the Galactic Motion Problem’. 相似文献
659.
Massimo Giovannozzi 《Celestial Mechanics and Dynamical Astronomy》1997,68(2):177-192
We study the stability domain of generic 2D area-preserving polynomialdiffeomorphisms. The starting point of our analysis is the study of thedistribution of stable and unstable fixed points. We show that the locationof fixed points and their stability type are linked to the degree of thepolynomial map. These results are based on a classification Theorem forplane automorphisms by Friedland and Milnor. Then we discuss the problem ofdetermining the domain in phase space where stable motion occurs. We showthat the boundary of the stability domain is given by the invariantmanifolds emanating from the outermost unstable fixed point of low period(one or two). This fact extends previous results obtained for reversiblearea-preserving polynomial maps of the plane. This analysis is based onanalytical arguments and is supported by the results of numericalsimulations. 相似文献
660.
选用山东 123 个国家级地面气象观测站 2007—2019 年地面逐小时降水资料,分析短时强降水分布特征,主要结论如下:1)其间共有 695 个短时强降水日、3 337 个短时强降水时次和 6 257 个短时强降水样本,基于排序法确定山东省极端短时强降水间值为 71.2 mm ? h-1,鲁东南地区间值最高,鲁中地区间值最低。2)各站年均发生 3.9 次短时强降水天气,鲁东南地区短时强降水和极端短时强降水发生频次最多,半岛地区短时强降水发生最少,鲁西南地区极端短时强降水发生最少。3)短时强降水集中出现在 6 月中旬至 8 月下旬,又以 8 月上旬最多。4)日变化显著,呈现典型 “双峰” 特征,主要集中在午后至傍晚,其次是后半夜;6 月中旬至 8 月下旬傍晚和后半夜发生短时强降水的可能性大,需重点关注。 相似文献