An analytical and numerical study of chaotic dynamics in a simple bouncing ball model

Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity-it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity.The Poincaré map,describing evolution from an impact to the next impact,is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically.     

基于电子水平仪的转轴倾角回转误差测量方法

测量竖直轴系倾角回转误差时,一般通过坐标系旋转法建立误差模型,利用傅里叶分析法分离误差得到。提出了基于几何学的倾角回转误差建模方法,得到了与坐标系旋转法一致的物理模型,建模过程更加简单。分别通过曲线拟合法和傅里叶分析法实现误差分离,并仿真分析了曲线拟合法和傅里叶分析法的误差分离精度。实验测得某型精密单轴转台倾角回转误差平均值、均方值分别为0.165″和0.186″,并得到各测量点处倾角回转误差实时测量值。     

Drag increment of internal waves generated by horizontally moving spheroid in supercritical regime

A theory on the drag increment of internal waves with a spheroid moving horizontally at a high velocity （or for large internal Froude number） in uniformly vertically stratified fluid （or ocean） is presented in the present paper. A surface source distribution is employed to model a hydrodynamic interaction between the spheroid and the stratified fluid. From theoretical results, it is shown that there exists an asymptote of zero-drag increment in supercritical regimes, where internal Froude numbers are larger than the critical internal Froude numbers. When the spheroid reduces to a sphere, the results in this paper is in good agreement with the previous theoretical and experimental results of the sphere.