运用球面解析理论分析了球面机构的位置正反解，并举例说明输入和输出之间的关系。
The forward and reverse position are analyzed by using the spherical analytic theory, and corresponding numerical examples are also given to show the relations between the inputs and the outputs.
只有发散球面波才是唯一稳定解。
他也得出了关于纵向对称运动和球面对称运动的类似解。
He also obtained similarity solutions for longitudinal and spherically symmetric motions.
用解球面三角形的方法，通过两天体的球面距离，求得星位角，从而求得船位的经纬度。
Through the solution, the star position angle can be found with so - called "star distance" (Short for the spherical distance between two stars)determined So as to have the fix solved.
通过在平面波谱域中比较复射线束叠加场和标准解的方法，导出了球面波和柱面波的复射线束展开系数公式。
In this article, we derive complex expansion formula of spherical and cylindrical waves by comparing the stacking field of complex ray and the close-form solution in the plane spectral domain.
在本文中，给出了方形积分区域上球面积的解析解，并在一极限条件下验证了该解析解的合理性。
In this paper, we give an analytical solution of the spherical area in the rectangular integral domain, and verify the validity of the solution under a limit condition.
在自由粒子的情况下给出了粒子的平面波解和球面波解。
The plane wave solution and spherical wave solution to free particles are also given.
回顾了并联机构位置正反解研究的数学基础，研究了2-DOF和3-DOF球面并联机构位置正反解问题；
The forward and inverse position problems of the 2-DOF and 3-DOF parallel spherical mechanism are studied.
根据光束传输的能量分配守恒法则和折射定律建立方程组，通过数学软件数值求解方程组，解得非球面矢高表达式。
The expression of aspheric surface is obtained by solving numerically equations based on law of conservation of energy and refraction law by mathematical software.
根据光束传输的能量分配守恒法则和折射定律建立方程组，通过数学软件数值求解方程组，解得非球面矢高表达式。
The expression of aspheric surface is obtained by solving numerically equations based on law of conservation of energy and refraction law by mathematical software.
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