角函数

First, a program which can be used to obtain the encoder values of each joint D. C. servomotor and then change them into angular position is developed. By means of cubic spline, the angular velocity and angular acceleration are calculated.

本文开发了实时采集和转换机器人各关节的码盘值为角位移的程序，并提出了以三次样条函数求各关节角速度和角加速度的方法，提高了计算精度。

A tapered incident wave is used to reduce the truncated error. The angular correlation function is calculated by Monte-Carlo generated rough surface, the enhancement on nonmemory line of the ACF can be used to detection a target placed over or under the rough surface.

在散射目标存在时，目标与粗糙面的复合多次散射场的角相关函数，在不满足记忆线条件下也有普遍较高的角相关函数值，即在非记忆线上的增强可以用于检测粗糙面上方、下方的散射目标。

For non-Kolmogorov turbulence, the anisoplanatiam error, the angular correlation function of Zernike polynomials, the residual phase structure function and the long-exposure OTF after low-order modes correction are analyzed.

分析了非科尔莫戈罗夫湍流情况下，自适应光学系统低阶模式校正时的非等晕误差、泽尼克系数角相关函数、残余相位结构函数以及长曝光光学传递函数，并定义了一个新变量模式校正因子，用来有效评价目标非等晕误差对低阶模式校正自适应光学系统补偿效果的影响。

Convert relationship of prototype robot joint angle and equivalent model joint angle is presented based on the method of kinematics inverse solution. The Jacobian algorithm of redundant robot for achieving effective joint excursion is studied, which is fit for digital calculating. The grads projection algorithm of redundant robot multi optimizing capability function's proportion factor is deduced. The issues of apery arm robot singularity and joint self-movement are researched. The simulation experiment result of apery arm joint self-movement and line movement is presented.

因为七自由度拟人手臂机器人的建模比较困难，采用了在等效模型下求解其运动学逆解的方法，给出了原机器人机构关节角与等效模型关节角之间的转换关系；提出了一种适于数值计算的有效的求解有关节偏置的冗余度机器人Jacobian的算法，并在此基础上推导了冗余度机器人多优化性能指标函数的均衡比例因子梯度投影算法；研究了拟人手臂机器人的奇异问题和关节自运动问题；给出了拟人手臂进行关节自运动和进行直线轨迹跟踪的仿真实验结果。

These results reveal that, as an intrinsic property of the wave function of atoms, the angle of the probability distribution of the angular two-electron density is approximately equal to the bond angle of the molecular which usually can be explained by the hybridization theory.

结果显示，作为原子波函数的内禀性质，双电子密度最可几角分布的角度与通常由分子杂化轨道理论解释的相关原子的分子的结合键角近似相等。

The stiffness-strength and dynamic properties of the composite material barrel is the function of the winding angles and volume fractions of the composites and the winding angles can be determined by the optimization.

复合材料身管的刚强度和动力特性均是缠绕角和复合材料含量的函数；缠绕角可以通过优化设计的方法来确定。

Concretely speaking, using the irreducible tensor theory, we deuced the formulism for fine-structure energies of boron-like atoms in the ground and first excited states, which involves spin-orbit, spin-spin and spin-other-orbit interactions; completing all the angular integrations and spin summations needed, we make the final expression for fine-structure energies of boron-like atoms in the ground and first excited states in a combination of radial integrations. Afterwards, employing the wave functions we got in Chapter Three, we accomplished all the radial integrations and so obtained the fine-structure energies.

具体地说，利用不可约张量理论导出了类硼离子基态以及第一激发态的精细结构的表达式，给出了自旋-轨道、自旋-自旋、自旋-其它轨道相互作用等所涉及的所有角向积分和自旋求和的解析计算方法，完成了角向积分、自旋求和的计算，使类硼离子基态以及第一激发态精细结构能级最终可以表示为径向积分之和；在此基础上利用以前所得到的非相对论性波函数，进一步完成了所有径向积分的计算，从而得到了对应能级的精细结构的理论计算值。

Proceed to the next step again go further inquire into definition of Grotzach domain function, and apply qualities of Grotzsch domain function to in K-quasiconformal mappings of on extended complex plane, the angles delitational estimation theorem is obtained.

根据Grotzsch的区域函数的定义，对其概念认真分析和探讨，进而再对Grotzsch的区域函数作了进一步的研究，并把Grotzsch的区域函数的性质应用于扩充复平面上的K-拟共形映射中，获得了一个角偏差估计的定理。

Summary In this paper, a brief history review of works on the theory of electromagnetic flowmeters is given. A method named'Alternative iteraction method for approaching real boundaries'is presented to solve Laplace's equation with mixed boundary conditions in electromagnetic flowmeters. The orthogonal expansion is used to analyze weight vectors and flow distribition effects on the sensitivity of the flowmeters.

本文在总结和分析了前人在电磁流量计变送器方面的理论研究成果后，首次提出了"交替迭代逼近边界"的方法求解电磁流量计理论研究中遇到的Laplace方程的混合边界条件问题；采用正交函数展开的方法研究权函数以及被测流体速度分布不规则对仪表输出的影响；采用保角变换的方法首次求解出电磁流量计偏心环域上的权函数。

In this paper, the basic mathematical model was derived by means of two methods, the first is the twostar positioning algorithm in celestial navigation theory and the second is based on the gyro dynamics theory. The results from these two methods are identical and therefore are correct. The latitude is equal to the elevation-angle of the polar gyro. The course is the ideal output from the sensor fitted to the outer gimbal. The longitude is a function of the equator gyro's azimuth and elevation angles.

本论文用天文导航中的双星定位法和经典的陀螺力学原理两种方法建立了ESGM的基本数学模型，并且得到一致的结果，说明所建模型是正确的，即载体的纬度等于极轴陀螺主轴相对水平面的高度角，载体的航向等于极轴陀螺外环轴上角度传感器的理想输出，载体的经度是赤道陀螺的方位角和高度角的函数。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。