Exact analytic solution for the rotation of a rigid body having spherical ellipsoid of inertia and subjected to a constant torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.     

光电等高仪I型的国际合作总结

中国科学院陕西天台和俄罗斯东西伯利亚物理技术和无线电测量研究所之间所进行光电等高仪I型的国际合作持续了5年，共完成3个纲要的观测。根据这些观测资料，编算出包括817颗星的无赤纬盲区的等高仪星表和24颗射电星的星表。在此对不同的系统差进行了分析。     

“三苗日食”的可能年代

史载上古禹时日妖宵出被解释为日落时发生的日食。分析了相关史料、该日食的各种可能年代及其戌地球自转长期变化的关系。     

用Lageos卫星SLR资料解算地球定向参数及监测地球质心的运动

利用Lageos卫星(1993～2002期间)全球激光测距资料精确测定地球定向参数及地心的变化,并将EOP(SHA)序列的结果与同期的EOP(IERS)C04进行比较,符合程度:极移XP-O.39 mas,yP-0.41 mas,日长Dr在0.03 ms左右.地心在X,y方向大约有1 cm左右的变化,在Z方向有3～4 cm左右的变化.     

火试金捕集等离子体发射光谱法测定铜铅电解阳极泥中铂和钯

采用火试金分离捕集,电感耦合等离子体发射光谱法分析了铜铅电解阳极泥中的铂和钯,重点试验了银的沉淀分离条件,方法应用于实际样品的分析,加标回收率大于95%。用贫铂矿国家一级标准物质和铜阳极泥管理样分析验证方法,其结果与标准值相符。方法的精密度(RSD,n=5)分别为Pt2.68%~3.04%,Pd4.55%~8.36%。     

The elastic distortion problem with large rotation in discontinuous deformation analysis

Conventional discontinuous deformation analysis (DDA) results in a change of block volume, which is known as free expansion, during rotation calculations because of the use of a linear displacement function to simulate the behavior of a block with a rigid body and elastic behaviors. This study demonstrates that the linear displacement function also generates unsolved elastic distortion, especially when the block undergoes large rotation in each calculation step. The distortion disturbs the contact judgment in the open–close iteration and update calculations of vertex coordinates, stresses, velocities, etc. at the end of each calculation step. A new procedure follows the flow chart of the original DDA, but it adopts additional codes for the coordinate-transformation calculations in vertex coordinate, stress, and velocity updates. When the vertex coordinates are updated, vertex displacements caused by strains are calculated before involving the block-rotation term in the displacement function to mitigate the elastic distortion. In addition, new codes compile formulas to transform stresses and velocities with block rotation. The new DDA ensures the correctness of rotating elastic calculations to solve practical falling rock problems with a large rotational angle in each calculation step.     

SOMATOM PLUS全身CTX线管旋转阳极及其控制电路的工作原理及维修

Ｘ线管是ＣＴ中最重要、最昂贵同时也是最易损坏的部件之一，而旋转阳级又是Ｘ线管中故障率最高的部件。因此正确判断Ｘ线管旋转阳级的故障显得尤为重要。如判断失误，将会给用户造成巨大的经济损失。本文阐述西门子ＳｏｍａｔｏｍＰｌｕｓ全身ＣＴ的旋转阳极及其控制电路的工作原理及维修方法，并以流程图的形式给出了步骤。     

阿尔金断裂走滑作用对青藏高原东北缘山脉形成的古地磁证据

通过对青藏高原北部阿尔金断裂东缘早白垩世-第三纪红层与玄武岩38个采点的系统古地磁测定,获得了研究区早白垩世-第三纪高温特征剩磁分量。结果表明,昌马乡早白垩世红层与玄武岩剖面层面坐标下高温特征剩磁平均方向(Ds=32.8°,Is=59.4°,κs=36.2,α95=8.1°)和北大窖早白垩世玄武岩剖面层面坐标下高温特征剩磁平均方向(Ds=335.4°,Is=55.1°,κs=34,α95=9.6°)均通过了褶皱检验,可能代表岩石形成时的原生剩磁。旱峡地区早白垩世地层层面坐标下高温特征剩磁平均方向(Ds=26.1°,Is=49.5°,κs=28.6,α95=7.3°)和红柳峡早第三纪地层层面坐标下高温特征剩磁平均方向(Ds=355.4°,Is=48.3°,κs=135.8,α95=7.9°),这两组高温特征剩磁方向在地理坐标下均远离现代地磁场方向,且具有正、反双极性特征,说明其也可能代表了岩石形成时的原生剩磁方向。结合已有阿尔金断裂及周边早白垩世-第三纪古地磁结果,提出柴达木块体在新生代印度/欧亚大陆碰撞挤压下并没有发生明显的整体顺时针旋转作用,青藏高原东北地区的块体旋转作用是阿尔金断裂左旋走滑作用在青藏高原东北缘转换的重要表现形式。     

A possible YORP effect on C and S Main Belt Asteroids

A rotating frequency analysis in a previous paper, showed that two samples of C and S-type asteroids belonging to the Main Belt, but not to any families, present two different values for the transition diameter to a Maxwellian distribution of the rotation frequency, respectively 48 and 33 km. In this paper, after a more detailed statistical analysis, aiming to verify that the result is physically relevant, we found a better estimate for the transition diameter, respectively D_C = 44 ± 2 km and D_S = 30 ± 1 km. The ratio between these estimated transition diameters, D_C/D_S = 1.5 ± 0.1, can be supported with the help of the YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect, although other physical causes cannot be completely ruled out.In this paper we have derived a simple scaling law for YORP which, taking into account the different average heliocentric distance, the bulk density, the albedo and the asteroid “asymmetry surface factor”, has enabled us to reasonably justify the ratio between the diameters transition of C-type and S-type asteroids. The same scaling law can be used to estimate a new ratio between the bulk densities of S and C asteroids samples (giving ρ_S/ρ_C ≈ 2.9 ± 0.3), and can explain why the asteroids near the transition diameter have about the same absolute magnitude. For C-type asteroids, using the found density ratio and other estimates of S-type density, it is also possible to estimate an average bulk density equal to 0.9 ± 0.1 g cm⁻³, a value compatible with icy composition. The suggested explanation for the difference of the transition diameters is a plausible hypothesis, consistent with the data, but it needs to be studied more in depth with further observations.     

Using sparse photometric data sets for asteroid lightcurve studies

With the advent of wide-field imagers, it has become possible to conduct a photometric lightcurve survey of many asteroids simultaneously, either for that single purpose (e.g., Dermawan, B., Nakamura, T., Yoshida, F. [2011]. Publ. Astron. Soc. Japan 63, S555–S576; Masiero, J., Jedicke, R., ?urech, J., Gwyn, S., Denneau, L., Larsen, J. [2009]. Icarus 204, 145–171), or as a part of a multipurpose survey (e.g., Pan-STARRS, LSST). Such surveys promise to yield photometric data for many thousands of asteroids, but these data sets will be “sparse” compared to most of those taken in a “targeted” mode directed to one asteroid at a time.We consider the potential limitations of sparse data sets using different sampling rates with respect to specific research questions that might be addressed with lightcurve data. For our study we created synthetic sparse data sets similar to those from wide-field surveys by generating more than 380,000 individual lightcurves that were combined into more than 47,000 composite lightcurves. The variables in generating the data included the number of observations per night, number of nights, noise, and the intervals between observations and nights, in addition to periods ranging from 0.1 to 400 h and amplitudes ranging from 0.1 to 2.0 mag.A Fourier analysis pipeline was used to find the period for each composite lightcurve and then review the derived period and period spectrum to gauge how well an automated analysis of sparse data sets would perform in finding the true period. For this part of the analysis, a normally distributed noise level of 0.03 mag was added to the data, regardless of amplitude, thus simulating a relatively high SNR for the observations. For the second part of the analysis, a smaller set of composite curves was generated with fixed core parameters of eight observations per night, 8 nights within a 14-day span, periods ranging from 2 to 6 h, and an amplitude of either 0.3 mag or 0.4 mag. Individual data sets using these fixed parameters added normally-distributed noise of 0.05, 0.1, or 0.2 mag. The analysis examined the success rates for finding the true period as the noise increased towards levels simulating data for objects close to sky background levels.After applying a filter to remove highly-ambiguous solution sets, the best chance for success was found to be when the true period was in the range of P ≈ 2–5 h and amplitudes were A ? 0.5 mag. The solution sets for lightcurves with low amplitude, long periods, and/or those that were sampled too sparsely in comparison to the period were often too ambiguous to be considered reliable for statistical rotation studies. Analysis of slow rotators (P > 24 h) found that somewhat reasonable solutions of P < 6 h could be found for about 15–20% of those objects, even at higher amplitudes, indicating that the Fourier analysis had locked onto the noise in the data.Efforts to produce an automated pipeline to help determine an unambiguous (or nearly so) solution based on the period spectrum from the Fourier analysis were made. These proved unsuccessful because of the number of parameters that must be considered and the difficulties in assigning an objective weight to each one in finding a final result. Despite this initial failure, further attempts will be made to quantify the U rating system.Comparison of the synthetic data analysis results to those from two actual surveys shows a reasonable agreement between the two. A review of the pros and cons of sparse versus dense data sets shows that each has a significant role in future studies and that it will be critical to establish open lines of communications and data exchange between the deep wide-field sparse data surveys and dense data programs.