Study of resonances for the restricted 3‐body problem     

B. Quarles  Z.E. Musielak  M. Cuntz 《Astronomische Nachrichten》2012,333(7):551-560

Our aim is to identify and classify mean‐motion resonances (MMRs) for the coplanar circular restricted three‐body problem (CR3BP) for mass ratios between 0.10 and 0.50. Our methods include the maximum Lyapunov exponent, which is used as an indicator for the location of the resonances, the Fast Fourier Transform (FFT) used for determining what kind of resonances are present, and the inspection of the orbital elements to classify the periodicity. We show that the 2:1 resonance occurs the most frequently. Among other resonances, the 3:1 resonance is the second most common, and furthermore both 3:2 and 5:3 resonances occur more often than the 4:1 resonance. Moreover, the resonances in the coplanar CR3BP are classified based on the behaviour of the orbits. We show that orbital stability is ensured for high values of resonance (i.e., high ratios) where only a single resonance is present. The resonances attained are consistent with the previously established resonances for the solar system, i.e., specifically, in regards to the asteroid belt. Previous work employed digital filtering and Lyapunov characteristic exponents to determine stochasticity of the eccentricity, which is found to be consistent with our usage of Lyapunov exponents as an alternate approach based on varying the mass ratio instead of the eccentricity. Our results are expected to be of principal interest to future studies, including augmentations to observed or proposed resonances, of extra‐solar planets in binary stellar systems (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

复杂性科学在页岩油气勘探和研究中的应用          下载免费PDF全文

于炳松  阮壮 《地质论评》2022,68(5):2022102012-2022102012

复杂性科学是当今世界科学重要的前沿领域之一。为了促进复杂性科学的基本理论和方法在页岩油气勘探和研究领域的广泛应用，笔者等重点围绕地质系统复杂性的基本内涵，从地质系统构成单元的多重耦合和相互作用、地质作用的复杂时空结构、地质作用过程中的自组织临界过程动力学以及矿产资源形成在混沌边缘等方面，介绍了地质系统复杂性研究的基本理论和研究方法。将上述地质系统复杂性理论运用于页岩油气系统，探讨了利用复杂系统的总体特征通过局域组成单元相互作用的“涌现”机制，来解决目前页岩储层中存在的如何利用微观局域精细表征进行客观刻画宏观储层特征问题；分析了利用地质作用的时空结构理论，建立页岩储层非均质性的静态和分形时空结构的方法；在整体论思想指导下，根据地质系统在混沌边缘分形生长这一规律，探讨了页岩油气在自组织临界态的混沌边缘富集预测方法。复杂性科学的理论和方法，必将在页岩油气的勘探研究中发挥越来越重要的作用。  相似文献