如何利用Mathematica7.0设计内摆线轨迹动态模型

根据内摆线的形成原理,利用Mathematica7.0模拟内摆线的形成轨迹.通过可读程序中对参数的不同取值,能够为多种内摆线轨迹提供模拟环境,进而为机械工程、实验教学等领域提供一种实用的分析工具.     

摆线

摆线是数学中众多的迷人曲线之一．它是这样定义的：一个圆沿一直线缓慢地滚动，则圆周上一固定点所描出的轨迹称为摆线．     

摆线

摆线是数学中众多的迷人曲线之一．它是这样定义的：一个圆沿一直线缓慢地滚动,则圆周上一固定点所描出的轨迹称为摆线．     

摆线及其相关问题

本文从摆线的定义及分类（分为平面摆线,摆线,内摆线,外摆线和球面摆线）出发,阐述了摆线的重要性质及其应用实例。其中摆线的几何性质包括：摆线的切线过动圆的顶点,摆线的法线过动圆的底点,摆线的切线与竖直线之间夹角的正弦和切点高的平方根之比是一个常数;摆线的物理性质包括等时性质和最速降线性质。最后给出应用实例。     

三种平面曲线的关系

本文讨论了三种重要的平面曲线———摆线、圆的渐开线与外摆线的关系。在文 [1 ]的基础上指出了前两种平面曲线都是外摆线的极限情况     

带电粒子在正交电磁场中运动问题的初步研究

在高中物理中常见到带电粒子在互相正交的磁场与电场中运动这类习题。但对带电粒子在正交的电磁场中运动的轨迹是怎样的这一问题，由于涉及高等数学知识，无法对高中学生说清楚，因此在分析问题时往往只介绍说其轨迹为摆线（旋轮线）就不再深究。其实，应用摆线的特征结合初等数学知识也可以推导其运动轨迹方程，这对理解其运动，     

三种平面曲线的关系

本文讨论了三种重要的平面曲线－摆线、圆的渐开线与外摆线的关系。本文[1]的基础上指出了前两种平面曲线都是外摆线的极限情况。     

摆线的几何画板实现

摆线被称为“几何学中的海伦”，在物理中称为“最速降线”。摆线是一类重要的曲线，齿轮的齿的纵断面、偏心轮、偏凸轮以及许多机器零件的轮廓线都是摆线，摆线的实用价值与椭圆、抛物线等曲线相比毫不逊色。因此，作为一类重要的曲线，摆线走进了《坐标系与参数方程》（《普通高中数学课程标准（实验）》系列4）。对此，《课标》明确要求：“借助教具或计算机软件，观察圆在直线上滚动时圆上定点的轨迹（平摆线），了解平摆线的生成过程并能推导出它们的参数方程。通过阅读材料，     

带电粒子在正交电磁场中运动问题的初步研究

在高中物理中常见到带电粒子在互相正交的磁场与电场中运动这类习题.但对带电粒子在正交的电磁场中运动的轨迹是怎样的这一问题,由于涉及高等数学知识,无法对高中学生说清楚,因此在分析问题时往往只介绍说其轨迹为摆线(旋轮线)就不再深究.     

椭圆摆线

摆线虽有长摆线、短摆线;内摆线、外摆线等不同种类,但它们都是由圆的滚动而得到的这些圆摆线的有关理论是众所周知的、本文将定义一种椭圆摆线,建立它的方程,并证明它具有与普通圆摆线类似的两条基本性质。 1 用角尺找圆心的启示工人常用角尺来作出一个圆形工件的圆心,其方法如图1.在用这种方法作圆心的过程中,若不变动直角顶点P的位置,如图2,同样可得到圆心Q的位置。更一般地,对圆     

基于模型参考自适应的一类二维系统形状渐近跟踪控制

针对二维线性系统,探究可实现其状态轨迹形状与参考系统状态轨迹间形状渐近跟踪的控制方法。首 先,利用刚体运动描述系统状态轨迹的形状渐近跟踪概念,然后对传统模型匹配条件进行扩展。在该条件下,采用 Lyapunov 稳定性与模型参考自适应相结合的方法,设计形状渐近跟踪控制器。实验表明,该控制器可保证被控系统与参考系统状态轨迹达到形状渐近跟踪。与传统方法相比,所给出的模型匹配条件及形状渐近跟踪控制器适用范围更广。最后,对模型进行仿真实验,证明了该控制方法的有效性。     

基于Fluent的离心分离腔体内流场模拟仿真

为研究离心式分离腔体内部气流流动轨迹以及梗丝颗粒的运动规律,进一步深入研究梗丝分离效果,基于ANSYS建立流体域模型,利用流体仿真软件Fluent,采用RNG湍流模型模拟腔体内气流轨迹,拉格朗日离散相模型（DPM）模拟颗粒相运动规律,得到腔体内气流轨迹、压力和颗粒相运动轨迹云图,并在入口处设定不同大小的气流速度,当入射速度为6m/s时,气流流动轨迹发生改变,达到8m/s时气流轨迹比较理想,且颗粒运动轨迹正确。此时梗丝在离心分离腔体内可以得到有效分离,梗中含丝率降低到2.55%左右,烟丝利用率进一步提高。     

Estimation of a Nonlinear Intervention Phase Trajectory for Multiple-Baseline Design Data

A multilevel logistic model for estimating a nonlinear trajectory in a multiple-baseline design is introduced. The model is applied to data from a real multiple-baseline design study to demonstrate interpretation of relevant parameters. A simple change-in-levels (ΔLevels) model and a model involving a quadratic function (Quadratic) for the nonlinear intervention phase data were also estimated. In addition, a simulation study was conducted to assess Markov chain Monte Carlo estimation of the logistic model and compare its trajectory recovery with use of the ΔLevels and Quadratic models. While most of the logistic model's parameter values were recovered well, trajectory recovery was very reasonable using the simpler Quadratic model. Results are discussed along with recommendations for practitioners and directions for future research.     

喷枪最优轨迹规划数学模型的建立

喷枪最优轨迹规划问题的目的是要确定一条使得工件表面涂层厚度差异达到最小的喷枪最优轨迹，本文对于由此建立的具体数学模型进行了详细阐述。     

Trajectories of Boys' Physical Aggression, Opposition, and Hyperactivity on the Path to Physically Violent and Nonviolent Juvenile Delinquency

A semi-parametric mixture model was used with a sample of 1,037 boys assessed repeatedly from 6 to 15 years of age to approximate a continuous distribution of developmental trajectories for three externalizing behaviors. Regression models were then used to determine which trajectories best predicted physically violent and nonviolent juvenile delinquency up to 17 years of age. Four developmental trajectories were identified for the physical aggression, opposition, and hyperactivity externalizing behavior dimensions: a chronic problem trajectory, a high level near-desister trajectory, a moderate level desister trajectory, and a no problem trajectory. Boys who followed a given trajectory for one type of externalizing problem behavior did not necessarily follow the same trajectory for the two other types of behavior problem. The different developmental trajectories of problem behavior also led to different types of juvenile delinquency. A chronic oppositional trajectory, with the physical aggression and hyperactivity trajectories being held constant, led to covert delinquency (theft) only, while a chronic physical aggression trajectory, with the oppositional and hyperactivity trajectories being held constant, led to overt delinquency (physical violence) and to the most serious delinquent acts.     

Enumeration Index Performance in Generalized Growth Mixture Models: A Monte Carlo Test of Muthén’s (2003) Hypothesis

Relatively few empirical studies have examined the performance of enumeration indices in correctly identifying longitudinal population heterogeneity when present, and these studies have produced mixed results. In light of these findings, Muthén (2003) suggested that the inclusion of time-invariant (antecedent) and time-varying (concurrent) covariates, as well as allowing the extracted growth mixture classes to predict a distal outcome (consequent covariate), could improve the performance of enumeration indices. This Monte Carlo simulation study examined the performance of a large set of enumeration indices within these generalized growth mixture model (GGMM) conditions, as suggested by Muthén, by manipulating 4 design conditions: (a) sample size, (b) separation distance between adjacent latent growth trajectories, (c) growth trajectory membership proportions, and (d) the amount of mixture model variance explained by the covariates. The findings suggest: (a) at smaller (N = 500) sample sizes, enumeration indices were much more likely to select an incorrect model than the correct one, (b) at larger (N = 3,000) sample sizes, correct model identification occurred only in the largest separation distance and trajectory membership equality conditions, and (c) the inclusion of covariates had a negligible effect at smaller sample sizes, but covariate inclusion had a more favorable effect on data generation model identification in the largest sample size, largest trajectory separation distance, and equal trajectory membership proportions conditions. Suggestions for researchers and future empirical study possibilities are discussed.     

On the Trajectories of the Predetermined ALT Model: What Are We Really Modeling?

This article shows that the mean and covariance structure of the predetermined autoregressive latent trajectory (ALT) model are very flexible. As a result, the shape of the modeled growth curve can be quite different from what one might expect at first glance. This is illustrated with several numerical examples that show that, for example, a linear trajectory might be present among the model predicted scores even though no latent change parameter was included in the model. In addition, 2 examples are given that show that the predetermined ALT model can fit to data generated by models with model structures that are rather different from that of the ALT model itself. The practical relevance of these findings is demonstrated using an empirical example. We end by providing recommendations for researchers considering the use of the predetermined ALT model.     

基于运动相似性的仿人机器人动作规划研究综述

阐述了基于运动相似性的仿人机器人动作规划研究进展：首先,分析了捕获人体运动轨迹,包括运动捕获设备类型与运动轨迹处理;其次,阐述了人机运动模型构建,包括运动重定向、分解与重构运动姿势;再次,阐述了不一致的目标环境控制,包括地面碰撞控制、不一致的形态控制、自适应学习、非线性连续运动轨迹设计等;最后进行了总结。     

基于多模式轨迹和车速自适应的变道超车规划

针对智能汽车变道超车规划中轨迹模式和速度策略单一的问题,提出一种安全高效、多模式轨迹和车速自适应的变道超车规划方案。通过建立可调参数的三段式变道超车模型,利用五次多项式设计变道轨迹拟合算法,以安全性为要求设计侧翻约束和碰撞约束边缘条件。基于多目标优化函数进行多模式轨迹优化,得到不同模式变道轨迹的解集空间,并基于超车阶段的时间进行速度自适应规划。通过MATLAB/Simulink构建仿真测试试验,结果表明该方案在全速域,满足安全条件约束下,能输出3种模式(效率模式、舒适模式和综合模式)的变道超车轨迹,输出的轨迹特性稳定,在两车相对速度较小时自适应速度规划能够有效提升超车效率。     

一种类人型机器人踢球时腿部轨迹规划实验方案

提出一种类人型机器人踢球时腿部运动的轨迹规划实验方案。在分析人踢球技术要点的基础上,综合考虑机器人的动力学模型和关节电机力矩约束,得出机器人踢球时的最大速度,用五次样条曲线规划出关节空间的平滑运动轨迹,并保证一定的加加速度,不易引起振动。