查询词典 curvature of curve

The Fary-Milnor theorem states that the total curvature of a knotted simple closed curve in R^3 is greater than 4π.

Fary-Milnor 定理：一条空间中的简单封闭扭结其总曲率必大於4π。

As we known, the total curvature of a simple closed plane curve γ is ±2π, that is,∫γ kds =±2π, from Cauchy-Schwarz's inequality, one gets that We will use Minkowski's support function to study the stability of the above

我们将利用Minkowski支撑函数，在Hausdorff距离的意义下研究这一不等式的稳定性。

If the change of step-size is controlled by the value of curvature of integral curve, the result can avoid such an error accumulation.

定步长的缺点在于不管是积分曲线的各个点的曲率如何都取一样的步长，这样肯定会在曲率大的一些点带来比较严重的误差，这种误差将在每一步的计算中积累。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

Its principle is that the turning points of the curve are decided by the sign and the magnitude of τ, the relative curvature of y=f, and T=yxn/(1+y'x2)3/2, where x=lg△K, y=lg.

其原理是：根据y=f的相对曲率τ=y_x~n/1+y_x~(′2~(3/2)的正负和大小来判定曲线的转折点，这里x=1g，y=Ig。

A new auto-stepping scheme based on the curvature of the solution curve is proposed, with which the course of tracing the nonlinear solutions will become more reasonable and more efficient.

对增量-迭代过程当中的弧长控制方法和迭代方法分别进行了深入研究，取得的成果有：1）提出一种新的弧长控制方案，消除了以往方案存在的漏洞。2）提出一种基于解曲线曲率的自动走步方案，使得整个的非线性追踪过程合理化，从而极大地提高了效率。

The basic frequences of the two types of bridges are heightened by increasing vertical curve curvature of stiffening girder, setting vertical supporting members and stiffing connection.

增大加劲梁竖曲线曲率，桥塔处设置竖向支撑和缆梁跨中固结均能提高悬索桥的自振基频。

After that the contour is produced by curve fitting and the curvature of every point of the contour is calculated.

然后，用曲线拟合轮廓线，并计算曲线上各点的曲率。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r&‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。