Normal forms for the epicyclic approximations of the perturbed Kepler problem

We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward.     

Ecohydrological change mechanism of a rainfed revegetation ecosystem at southeastern edge of Tengger desert,Northwest China

Study is made on a 45 km-long artificial ecosystem without irrigation in Tengger desert on the basis of long-term ecological monitoring and ecohydrological fundamentals.Changes in water allocation, utilization, cycle and balance patterns in more than 40-year evolution of the soil-plant system are analyzed. The formation of a drought horizon in shrub rhizosphere and its effect, ecohydrological function of the crust and its effect on the soil-plant system change are discussed. Driven by water self-regulation and water stress, the soil-plant system is going to develop towards the steppe desert to ensure more effective use and optimum collocation of water resource.     

电子地图业在卫星导航应用中的发展对策研究

本文分析了卫星导航应用中与地理信息产业相关的电子地图产业在国内外发展的现状与趋势,研究了新时期中国导航电子地图业的基本特征和作用,提出了电子地图产业的发展对策。     

人工抽水引起土洞塌陷的可能性

在人工抽水过程中,抽水量越大、距抽水井越近,越可能产生土洞塌陷.在砂土层中,抽水持续时间越长,地下水潜蚀作用越强,越有可能产生土洞塌陷;在粘性土层中,避免反复频繁抽水及适当减少抽水初期的抽水量,有利于减少土洞塌陷的可能性.     

Adiabatic chaos in the Prometheus–Pandora system

The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical–experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.