The influence of the orbital eccentricity of a primary on the chaotic region     

Liu Jie 《Chinese Astronomy and Astrophysics》1991,15(4):446-448

Applying the resonance overlap theory to the elliptic three-body model, it is shown that the effect of the eccentricity is to increase the size of the chaotic region.  相似文献   

Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem     

D. Viswanath 《Celestial Mechanics and Dynamical Astronomy》2006,94(2):213-235

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses 1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for μ small enough in the unaveraged restricted three-body problem.  相似文献   

The integrable cases of the planetary three-body problem at first-order resonance     

V. N. Shinkin 《Celestial Mechanics and Dynamical Astronomy》1993,55(3):249-259

This paper investigates the stability of the motion in the averaged planar general three-body problem in the case of first-order resonance. The equations of the averaged motion of bodies near the resonance surface is obtained and is analytically integrated by quadratures. The stability of the averaged motion is analytically investigated in relation to the semi-major axes, the eccentricities and the resonance phases. An autonomous second-order equation is obtained for the deviation of semiaxes from the resonance surface. This equation has an energy integral and is analytically integrated by quadratures. The quasi-periodic dependence on time with two-frequency basis of the averaged motion of bodies is found. The basic frequencies are analytically calculated. With the help of the mean functionals calculated along integral curves of the averaged problem the new analytic first integrals are constructed with coefficients periodic in time. The analytic conditions of librations of resonance phases are obtained.  相似文献   

Mapping models for near-conservative systems with applications     

Ji-Lin Zhou  Yan-Ning Fu  Yi-Sui Sun 《Celestial Mechanics and Dynamical Astronomy》1994,60(4):471-487

A systematic method is presented to construct a mapping model for a near-conservative system, based on that of Hadjidemetriou for a Hamiltonian system [1]. The mapping we constructed preserves the basic features of the actual system. We apply this method to the forced oscillating system and to the 3 : 1 resonant grain motion in the presence of Poynting-Robertson drag.Supported by the National Natural Science Foundation of China.  相似文献   

Forced secondary resonances at the 3 : 1 commensurability     

Yi-Sui Sun  Ji-Lin Zhou  Tian-Ling Zhang  Chong-Qing Cheng 《Celestial Mechanics and Dynamical Astronomy》1994,59(4):313-325

For the 3 : 1 Jovian resonance problem, the time scales of the two degrees of freedom of the resonant Hamiltonian are well-separated [5]. With the adiabatic approximation, the solution for the fast oscillations can be found in terms of the slowly varying variables. Thus the rapidly oscillating terms in the slow oscillation equations can be treated as forced terms. We refer to the resonance between the forcing and intrinsic frequencies as a forced secondary one in this paper. We discuss the forced secondary resonances in asteroidal motion at the 3 : 1 commensurability by using Wisdom's method. The results show that the orbits situated originally near the resonance will leave the neighbourhood of resonance and tend to the separatrices and critical points for different energies, respectively. We have not found any stochastic web as expected in this case. Moreover, we study the problem of validity on the approximation of a system.The Project Supported by the National Natural Science Foundation of China.  相似文献   

Surfaces of section in the Miranda-Umbriel 3:1 inclination problem     

Michèle Moons  Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1994,59(2):129-148

The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermottet al. (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 inclination resonance between Miranda and Umbriel is analysed.  相似文献   

Novel Analysis of Tadpole and Horseshoe Orbits     

Jan Vrbik 《Celestial Mechanics and Dynamical Astronomy》1997,69(3):283-291

A simple analysis of tadpole and horseshoe orbits is performed using a new perturbation technique. The first-order results are presented explicitely, extension to any perturbation order is delineated. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

Revisiting natural and laboratory electron spin resonance (ESR) dose response curves of quartz from Chinese loess     

《Quaternary Geochronology》2022

Natural and laboratory ESR dose response curves (DRCs) of [AlO₄/h]⁰ and [TiO₄/M⁺]⁰ were investigated for samples of quartz from the Luochuan loess-palaeosol master section, Chinese Loess Plateau. The natural and laboratory DRCs show a clear divergence above ∼1000 Gy, with much lower D₀ values and saturation levels observed for the natural DRCs, which is in agreement with the previous study by Tsukamoto et al. (2018). Young (<15 ka) samples from Luochuan and Jingbian – another site of the Chinese Loess Plateau, together with two modern samples of Chinese loess, were used to investigate the residual signals of [AlO₄/h]⁰ and [TiO₄/M⁺]⁰ centres. Our results are in line with published studies and show that the significant residual signals corresponding to several tens to hundreds of Gy are present in both Al and Ti centres. These need to be taken into account before laboratory DRC construction. ESR pulse annealing experiments performed on samples irradiated with different doses show an apparent dose-dependent thermal instability of [AlO₄/h]⁰ and [TiO₄/M⁺]⁰, with the signals for higher doses decaying faster with increasing temperature. We attribute the change in D₀ with preheat reported in Tsukamoto et al.2018, as well as the difference between laboratory and natural DRCs, to this apparent dose-dependent thermal instability of the signals. The saturation level of the natural DRC, being the result of reaching the equilibrium between filling of the traps and emptying them due to thermal decay, is therefore additionally affected at higher doses, due to the increased thermal instability. The inability to recreate in the laboratory the same response to irradiation as the one observed in nature questions the accuracy of dating samples beyond ∼1000 Gy.  相似文献   

车装全液压钻机桅杆模态分析及拓扑优化          下载免费PDF全文

杜垚森  和国磊  冯起赠  赵远  师敏  宋志彬  朱芝同  刘晓林  许本冲  秦如雷  马汉臣  伍晓龙  高鹏举  汤小仁  王晓赛 《探矿工程》2022,49(3):70-75

车装全液压钻机具有自动化程度高、工艺适用范围广、机动性好及施工效率高等优点,因此被广泛应用于煤层气抽采井、水井等钻井施工。桅杆作为钻机的重要构件,支撑着动力头的回转钻进工作,桅杆工作振动的稳定性对钻机工作的可靠性具有十分重要的影响。通过对桅杆进行模态分析,明确了桅杆的固有频率和模态振型,结果表明桅杆可能发生共振现象;通过对桅杆进行拓扑优化分析,并且根据桅杆的实际功能,得到优化模型,静力分析和模态分析结果均表明优化效果显著,满足结构强度要求且避免了共振的发生。桅杆的有限元分析,为桅杆的结构设计提供了理论支撑,同时提供了一种现代机械结构设计方法,具有一定的参考意义。  相似文献   

Resonance trapping and evolution of particles subject to poynting-robertson drag: Adiabatic and non-adiabatic approaches     

R.S. Gomes 《Celestial Mechanics and Dynamical Astronomy》1995,61(1):97-113

The problem of resonance trapping for particles subject to Poynting-Robertson drag is approached initially from an adiabatic regime theory. A simplified Hamiltonian system is presented for simple eccentricity-type resonances up to order 3, and expressions related to the trapping process are deduced. The fast dissipation provoked by Poynting-Robertson leads to the employment of a numerical approach for the computation of resonance capture probabilities, for particles in the size range of practical importance. Some aspects of the dynamical evolution of a particle after capture are noticed from results of numerical integrations. Analytical methods are used in order to confirm the numerical results.  相似文献