Structures in the phase space of a four dimensional symplectic map

We numerically investigate the projections of non periodic orbits in a 4-dimensional (4-D) symplectic map composed of two coupled 2-dimensional (2-D) maps. We describe in detail the structures that are produced in different planes of projection and we find how the morphology of the 4-D orbits is influenced by the features of the 2-D maps as the coupling parameter increases. We give an empirical law that describes this influence.     

Resonant Periodic Orbits of Trans-Neptunian Objects

We study two and three-dimensional resonant periodic orbits, usingthe model of the restricted three-body problem with the Sun andNeptune as primaries. The position and the stability character ofthe periodic orbits determine the structure of the phase space andthis will provide useful information on the stability and longterm evolution of trans-Neptunian objects. The circular planarmodel is used as the starting point. Families of periodic orbitsare computed at the exterior resonances 1/2, 2/3 and 3/4 withNeptune and these are used as a guide to select the energy levelsfor the computation of the Poincaré maps, so that all basicresonances are included in the study. Using the circular planarmodel as the basic model, we extend our study to more realisticmodels by considering an elliptic orbit of Neptune and introducingthe inclination of the orbit. Families of symmetric periodicorbits of the planar elliptic restricted three-body problem andthe three-dimensional problem are found. All these orbitsbifurcate from the families of periodic orbits of the planarcircular problem. The stability of all orbits is studied. Althoughthe resonant structure in the circular problem is similar for allresonances, the situation changes if the eccentricity of Neptuneor the inclination of the orbit is taken into account. All theseresults are combined to explain why in some resonances there aremany bodies and other resonances are empty.     

Short-lived asteroids in the 7/3 Kirkwood gap and their relationship to the Koronis and Eos families

A population of 23 asteroids is currently observed in a very unstable region of the main belt, the 7/3 Kirkwood gap. The small size of these bodies—with the notable exception of (677) Aaltje (∼30 km)—as well as the computation of their dynamical lifetimes (3<T_D<172 Myr) shows that they cannot be on their primordial orbits, but were recently injected in the resonance. The distribution of inclinations appears to be bimodal, the two peaks being close to 2° and 10°. We argue that the resonant population is constantly being replenished by the slow leakage of asteroids from both the Koronis (I∼2°) and Eos (I∼10°) families, due to the drift of their semi-major axes, caused by the Yarkovsky effect. Assuming previously reported values for the Yarkovsky mean drift rate, we calculate the flux of family members needed to sustain the currently observed population in steady state. The number densities with respect to semi-major axis of the observed members of both families are in very good agreement with our calculations. The fact that (677) Aaltje is currently observed in the resonance is most likely an exceptional event. This asteroid should not be genetically related to any of the above families. Its size and the eccentricity of its orbit suggest that the Yarkovsky effect should have been less efficient in transporting this body to the resonance than close encounters with Ceres.     

Regression Formulations for the Stress at Hot Spot of Multiplanar Tubular DT Joints

- Stress concentration analysis of multiplanar tubular DT joints plays an important role in the fatigue design of offshore platforms. A semi-analytic method for stress analysis under the condition of any loads is briefly introduced in the paper. Nineteen multiplanar tubular DT joints with one of two braces of the same dimension subjected to axial loads and out- of- plane bending moments are computed for parametric stress analysis by using the present method. The influence of geometrical parameters on the stresses of multiplanar tubular DT joints is discussed and compared with corresponding uniplanar T joints. The regression formulae for the stress at hot spot of multiplanar DT joints are found by modification of SCF of corresponding uniplanar T joints. The parametric formulae for the maximum stress by superposition. Finally, the influences of stiffening effect and load-interaction effect on the maximum stress of DT joints are discussed.     

Nonlinear stability of the libration points in the photogravitational restricted three body problem

The stability of the triangular libration points in the case when the first and the second order resonances appear was investigated. It was proved that the first order resonances do not cause instability. The second order resonances may lead to instability. Domains of the instability in the two-dimensional parameter space were determined.     

A stability study of asteroid families near the 3:1 and 5:2 resonance with Jupiter

By using theD-criterion Lindblad (1992) has identified 14 asteroid families from a sample of 4100 numbered asteroids with proper elements from Milani and Kneevi (1990). Taxonomic types and other physical properties for a significant number of objects in five of the families show strong homogeneity within each family, further strengthening their internal relationship.To test the hypothesis of a common origin in, e.g., a catastrophic collision event, we have set out to integrate the orbits of the members of the Maria, Dora and Oppavia-Gefion families over some 10⁶ years. The mean distance for the Maria family is close to the 3:1 mean-motion resonance with Jupiter, while the other two families lie close to the 5:2 resonance.We used a simplified solar system model which included the perturbations by Jupiter and Saturn only and implemented Everhart's variable stepsize integrator RA15. All close encounters between the family members (within 0.1 AU) were recorded as well. Preliminary results from integrations over 4×10⁵ years are presented here.The statistics of close encounters show pronounced peaks for several members within each family, while for others no significant levels above the background of random encounters or even very low frequencies were found. This indicates a subclustering within the families. Quite a lot of very close (<0.005 AU) mutual encounters are found, which suggest that, at least for the larger members in a family, the mutual gravitational interactions could be of some importance for the real orbital evolutions.The encounter statistics between the Dora and Oppavia family members suggest a possible interrelationship between this two groups.     

参量阵浅地层剖面测量技术 在近岸海洋工程的应用效果

介绍了海底浅地层声学探测技术的发展情况, 简述了新型参量阵声纳探测的原理和特点, 通过SES-96参量阵测深或浅地层剖面系统在山东半岛海区的应用实例, 对此新型参量阵声纳技术的应用效果进行了分析评价。     

测量平差函数模型的若干讨论

讨论了测量平差函数模型的几种形式———参数模型、非参数模型及半参数模型 ,分别论述了各种模型的优缺点及其适用范围。半参数模型对于客观实际具有极强的解释能力 ,应给予充分的重视和深入的研究。     

Evaluating accuracy for two empirical methods in predicting settlement of drilled shafts

Several theoretical, empirical and semi-empirical methods are available in the literature to predict settlement of drilled shafts in sandy soils. In the Arabian Gulf countries, specifically in the United Arab Emirates, equations and procedure from the rest of the world are being used in analysis and design of drilled shafts without proper validation. It is the aim of this study to assess the applicability and evaluate the accuracy of two well known, and commonly used methods for pile prediction in the United Arab Emirates (UAE), namely Vesic (1977) and Poulos (1979), via comparison with data from field pile load tests conducted on shafts drilled in the region. Some of these tests were conducted for the purpose of this study, while others were made available through the courtesy of International Piling Contractors who are active in the region (e.g. Bauer International and Swiss Borings). Pile load test data were analyzed to back-calculate the model parameters related to settlement under different loading stages. Geological data and soil properties were obtained from studies conducted at the relevant sites. An effort is made to correlate soil properties with the prediction models. Statistical analysis is conducted to assess the accuracy of the results obtained from the two methods at different stages of loading via those obtained from pile load tests. Moreover, a detailed parametric study is conducted to assess the effect of the related parameters on the predicted pile settlement and the estimated settlement at different stages of loading. The study concluded with a recommendation of the most appropriate models and procedures to be followed for predicting the settlement of drilled shafts in the UAE, together with useful charts and correlation relations. Results showed that settlement values predicted by Vesic (1977) and Poulos (1979) overestimates the true values. This revised version was published online in July 2006 with corrections to the Cover Date.