A method for relaxing parameter constraints in rigid body dynamics

As attractive alternatives to a set of three Euler angles, the rotation of a rigidly deforming body is often represented using four or more parameters. The accompanying parameter constraints introduce generalized constraint forces in the equations of motion which can often negate the benefits of a particular parameterization. In this paper, we discuss situations where the parameter constraints are not imposed. Thus, although the body no longer deforms rigidly, it does deform homogeneously. This allows the theory of a Cosserat point (or, equivalently, the theory of a pseudo-rigid body) to be used to establish equations governing its motion. Earlier work on this topic by O’Reilly and Varadi considered the four Euler parameters and the single Euler parameter constraint. Here, we consider Poincaré's six parameter representation of a rotation tensor, and, complementing earlier work, discuss numerical implementation and representative simulations. One of the contributions of this paper is the development of a viscoelastic Cosserat point, whose equations of motion are free from parameter constraints and singularities, that can be used to approximate the motion of a rigid body.     

Phase Behavior of Methane-Pentane Mixture in Bulk and in Porous Media

The adiabatic calorimetry method is used to measure the isochoric heat capacity and the dew-bubble curves for the methane-normal pentane mixtures in bulk for three different mixture compositions of n-pentane. The near-critical behavior of the mixture heat capacity indicates that at low n-pentane concentrations, this system is close to the special point of the critical locus. The effect of porous medium has been investigated for one of the mixtures studied in bulk. It has been shown that in porous medium the essential shift of the dew-bubble curve takes place. In our opinion this shift is caused by the formation of wetting film on the surface of porous medium. The estimation of film thickness resulting from the data obtained yields the value 7–8 nm.     

新型挠性支承结构及其加工方法

在分析现有几种挠性支承结构和加工方法的优缺点的基础上，研究了一种新型的挠性支承结构并在充分分析这种结构的优点后，提出了针对这种结构的切实可行的加工方法。此外还讨论了这种加工方法所存在的问题。     

基于电子海图显示信息系统的惯性/地磁组合导航

为实现惯导系统长时间高精度导航,以性能优良的电子海图显示信息系统为开发背景,对地磁匹配辅助惯性导航系统进行了设计和仿真实验。在原有电子海图显示信息系统的基础上开发了数据采集模块、地磁数据库模块、惯导/地磁匹配模块、惯导误差估计模块等功能软件,并对各功能模块进行了深入分析。仿真试验结果证明,基于电子海图显示信息系统的惯性/地磁组合导航达到了校正惯性导航系统,实现高精度导航的目的。     

A COMPLETE EXPRESSION OF THE ASYMPTOTIC SOLUTION OF DIFFERENTIAL EQUATION WITH A∩-TH ORDER TURNING POINT

A second order linear ordinary differential equation has been studied, and the complete expresson, of the formal uniformly valid asymptotic solutions to the equation near turning point is obtained by using extended Airy function.     

域外奇点法在弹性力学中的应用

本文将域外奇点法推广应用于弹性力学问题,求解了扭转问题,平面弹性问题和平面弯曲问题.计算表明,这种方法简单,计算时间短,精度高。     

Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

Holomorphic Flows on Simply Connected Regions Have No Limit Cycles

The dynamical system or flow = f(z), where f is holomorphic on C, is considered. The behavior of the flow at critical points coincides with the behavior of the linearization when the critical points are non-degenerate: there is no center-focus dichotomy. Periodic orbits about a center have the same period and form an open subset. The flow has no limit cycles in simply connected regions. The advance mapping is holomorphic where the flow is complete. The structure of the separatrices bounding the orbits surrounding a center is determined. Some examples are given including the following: if a quartic polynomial system has four distinct centers, then they are collinear.     

软土地基变形的混沌性与承载力识别

本文以混沌理论为基础, 分析了软土地基变形的混沌性态, 并采用映射函数f(x)=ax²+c来拟合软土地基的沉降-载荷曲线。根据映射函数的不动点, 对软土地基加固前后的承载力进行了识别, 并与按相对变形值确定的承载力进行了比较。     

A criterion for the onset of growth of two shear cracks in an elastic body under plane-strain conditions

The Wiener-Hopf method is used to find a solution to a symmetric problem that gives a criterion for the onset of growth of long shear cracks emanating from a corner point on the boundary of a hole and filled with a plastic material __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 83–90, April 2006.