1·This paper presents a new method named "Analytic Orthogonalization", for orthogonalizing direction cosine matrix.
本文提出方向余弦矩阵正交化的一种新方法——解析正交化。
2·The coordinate transformation matrix based on the direction cosine parameters from the object coordinate system to the world coordinate system is derived by vector algebra.
利用矢量代数的方法，推导出以方向余弦为参量的物坐标系到世界坐标系的坐标变换矩阵；利用矩阵求逆的方法，推导出世界坐标系到物坐标系的坐标变换矩阵。
3·A kinematics model by post D-H method for 4R-robot was offered in this paper, which derived the manipulator finger position and its attitude with unit vectors of direction cosine.
采用D-H后置法建立了4R机器人运动方程，建立机器人执行机构在空间相对位置关系的数学模型，由此可解出手部位置和用单位矢量方向余弦表示的姿态。
4·Methods of spherical trigonometry and direction cosine matrix were applied respectively to derive the bracket error, and the two methods had the same error formula and the same calculation results.
应用球面三角法和方向余弦矩阵法分别推导出双轴陀螺平台的支架误差公式，发现由这两种方法推导出来的公式计算结果是一致的。
5·Then this is the component in your direction we call that the radial component which is v cosine theta.
这是y方向的，组成因素,我们称之为辐射组成,等于vcosθ
6·Since there is no acceleration in the y direction, the normal force must be also mg cosine theta.
既然在y方向上,没有加速度，法向力也等于mgcosθ
7·So this one equals m1 g cosine alpha - and this one, the x component-- which is in the minus x direction now-- equals m1 g sine alpha.
得到m1gcosα,而x方向上-,这里是x负方向-,大小是m1gsinα
8·Well, what I can change is the direction, and this will be the largest when the cosine is one.
我可以改变的是方向，当cos=1时，这个可以取到最大。