非线性弹性地基上圆形薄板三次超谐共振

本文研究非线性地基上圆形薄板受简谐激励的次谐波共振问题。按照弹性力学理论建立非线性地基上圆形薄板受简谐激励的动力学方程。利用Galerk in方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统满足3次超谐共振条件的一次近似解,并进行数值计算。分析阻尼、地基系数、调谐值、激励等参数对共振响应曲线的影响。     

Forty years of measurements of the mean magnetic field of the Sun: View from today

During the last 40 years, the Crimean Astrophysical Observatory and five other observatories around the world have carried out more than 18 500 (daily) measurements of the mean magnetic field (MMF) of the Sun as a star. The main MMF periodicity is due to the equatorial rotation of the Sun with a synodic period of 26.92 ± 0.02 day (it was stable for decades, but “bifurcated” in the 23rd cycle). It is shown that (a) the average sidereal period of the equator, 25.122 ± 0.010 day, is in close resonant relations with orbital and axial rotations of Mercury (5: 2 and 5: 3, respectively); (b) the most powerful long period, 1.036 ± 0.007 years, is suspiciously close to the orbital period of the Earth and (c) coincides with the average synodic period of revolution of giant planets 1.036 ± 0.020 years; and (d) MMF reveals a significant period of 1.58 ± 0.02 years, which agrees, within errors, with the synodic period of Venus (1.60 years), and (e) a significant periodicity of 19.8 ± 2.5 years probably related to the 22-year magnetic cycle of the Sun. The nature of all these periodicities is mysterious.The assumption is made that the resonances originated at the early stages of formation of the Solar System, and their existence in the modern epoch is due to the specific features of the structure and dynamics of the central core of our star. It is found that the MMF level averaged over 40 years is practically zero, ?0.018 ± 0.015 G. The anomalous behavior of the 23rd cycle is pointed out; this is expressed in (1) violation of the Gnevyshev-Ohl rule for the pair of cycles 22–23, (2) accelerated rotation of the solar equator by 1.2%, and (3) considerable increase in the cycle duration (not smaller than 11.5 years), as compared to the average cycle duration in the 20th century (11.5 years). The problem of the so called magnetic “monopole” of the Sun is briefly discussed.     

电离层舒曼共振的空间观测

通过功率谱分析和波阻抗函数计算,本文证实了Aureol 3卫星在电离层高度上(>600km)观测到的极低频(ELF)波场扰动是和舒曼共振相关的电磁振荡.与舒曼共振地面观测相比较,Aureol 3观测到的舒曼共振电场分量具有很好的谐振谱结构,峰值频率和各阶舒曼共振本征频率对应;磁场分量的高阶峰值频率偏离14, 20, 26Hz等舒曼共振本征频率;随着卫星高度的改变,电场与磁场谐振的一阶最大能量峰值并不会发生在同一频率,结合本文分析的数据,分别位于78Hz和10Hz;水平方向的磁场分量更接近南北方向的线极化而不是地球－电离层空腔中的椭圆极化;波阻抗随频率表现出不太规则的准正弦振荡,它会随着频率增加和飞行高度上升呈现减小的趋势.虽然舒曼共振信号和电离层密度梯度间的非线性作用可以解释舒曼共振空间观测的部分特征,但需加入其他机制,如电离层不稳定性,传播模式的耦合,进一步了解电离层高度上舒曼共振各种特征产生的原因.     

Can a globular cluster formed in the galactic disk be raised into the halo?

The classical assumption that most globular clusters (hereafter GC) formed in situ in galactic halos is examined in an approximate, empirical way. Although this viewpoint is not rejected per se, an alternative possibility is investigated: the presence of multiple resonances in the galactic disk, together with the concurrent action of a resonant internal bar or distortion, may stir these resonances. This may lead to chaotic motion which breaks the action of the third integral for moderately eccentric orbits. These circumstances may consequently allow the formation of some GC’s in the disk with moderate to highly eccentric orbits, with the action of the resonant bar subsequently gradually driving them (as well as other stars with similar orbits) to spend most of their time in the Galaxy’s halo. The size of the resonant region and the probable effectiveness of the various agents in the associated phase space in the axisymmetric model are listed. An n-body simulation would be required to establish this proposal in a fully self-consistent way. Paper presented at the Division of Dynamical Astronomy Meetings in Halifax, N.S., Canada, June 2006.     

Young Age for the Veritas Asteroid Family Confirmed?

We present a comprehensive analysis of the dynamics of Veritas family members located in a chaotic strip centeredat 3.174 AU. A total of 600 chaotic members of the family and their clones were integrated for 100 Myr, and the variation of the distance with respect to the barycenter of the family have been computed forall of them. A simple classification of the prevailing behaviors hasbeen introduced to help identify typical dynamical patterns and states that could affect an estimate of the upper bound to the age of the family. We pointed out the importance of the temporary captures in thequasi-stable states, which occur often enough to affect the statistical analysis of the exits. The results are compatible with the young age (<100 Myr) for the family of Veritas, but we cannot say precisely how young it really is. This revised version was published online in July 2006 with corrections to the Cover Date.     

Explicit Semianalytical Theory of Asteroid Motion

A new semianalytical theory of asteroid motion is presented. The theory is developed on the basis of Kaula's expansion of the disturbing function including terms up to the second order with respect to the masses of disturbing bodies. The theory is constructed in explicit form that gives the possibility to study separately the influence of different perturbations in the dynamics of minor planets. The mean-motion resonances with major planets as well as mixed three-body resonances can also be taken into account. For the non-resonant case the formulas obtained can be used for deriving the second transformation to calculate the proper elements of an asteroid orbit in closed form with respect to inclinations and eccentricities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Review of the dynamics in the Kirkwood gaps

The study of mean motion resonance dynamics was motivated by the search for an explanation for the puzzling problem of the Kirkwood gaps. The most important contributions in this field within the last 32 years are reviewed here. At the beginning of that period, which coincides with the first long-term numerical investigations of resonant motion, different hypotheses (collisional, gravitational, statistical and cosmological) to explain the origin of the gaps were still competing with each other. At present, a general theory, based on gravitational mechanisms only, is capable of explaining in a uniform way all the Kirkwood gaps except the 2/1 one. Indeed, in the 4/1, 3/1, 5/2 and 7/3 mean motion commensurabilities, the overlap of secular resonances leads to almost overall chaos where asteroids undergo large and wild variations in their orbital elements. Such asteroids, if not thrown directly into the Sun, are sooner or later subject to strong close encounters with the largest inner planets, the typical time scale of the whole process being of the order of a few million years. Unfortunately, this mechanism is not capable of explaining the 2/1 gap where the strong chaos produced by the overlapping secular resonances does not attain orbits with moderate eccentricity, of low inclination and with low to moderate amplitude of libration. In the light of the most recent studies, it appears that the 2/1 gap is the global consequence of slow diffusive processes. At present, the origin of these processes remains under study.     

Intermittent Trajectories in the 3/1 Jovian Resonance

The statistical behaviour of intermittent trajectories at the 3/1resonance is investigated. The elliptic planar restricted three-body problemis used as a model. Distribution functions for time intervals D betweeneccentricity bursts are obtained and theoretically interpreted. For smallervalues of D the distribution is found to be of Poisson type, while in itstail it is described by a power law D. This change in thedistribution occurs for values of D in the range10⁵10⁶Jupiter periods. The power-lawindexfor the integral distributions lies in the range (-2,-1) and istrajectory dependent. The algebraic decay in the tails of the distributionsis explained by the phenomenon of sticking of orbits to the chaos borderduring long intervals between bursts.     

Regular and Chaotic Solutions of the Sitnikov Problem near the 3/2 Commensurability

Regular solutions at the 3/2 commensurability are investigated forSitnikovs problem. Utilizing a rotating coordinate system and theaveraging method, approximate analytical equations are obtained for thePoincare sections by means of Jacobian elliptic functions and 3periodicsolutions are generated explicitly. It is revealed that the system exhibitsheteroclinic orbits to saddle points. It is also shown that chaotic regionemerging from the destroyed invariant tori, can easily be seen for certaineccentricities. The procedure of the current study provides reliable answersfor the long-time behavior of the system near resonances.