四元数

Due to the demand of the large angle attitude control, the unit quaternion is used to describe the spacecraft attitude in this thesis.

针对飞行器以姿控发动机作为姿控执行机构时的大角度姿态运动需求，本文采用单位四元数作为弹体姿态描述，考虑到姿控发动机布局对姿态控制的影响，直接以姿控发动机推力作为系统的控制输入，利用反馈线性化方法，将原非线性系统转化为一个六阶线性子系统和一个一阶内动态子系统。

The orientation-singularity expression of the Stewart platform is deduced by using unit quaternion which can avoid singularity when using Euler angles to represent the orientation of rigid body, and then the algorithm of orientation-workspace of the manipulator at a certain position is proposed.

基于单位四元数描述的刚体姿态，避免了欧拉角等描述刚体姿态的奇异性问题，推导出Stewart机构处于给定位置时的姿态奇异解析表达式，并提出了该机构处于给定位置时的姿态工作空间算法，通过计算机仿真给出该机构处于一给定位置时姿态奇异轨迹和姿态工作空间的三维可视化描述。

After the data collection finished, it send to the PC through RS232 serial port. It gets the relatively high acceleration of the equipment, basing on the quaternion equation of the mathematics platform, and through the calculation of the angle changing and the acceleration sensor send-out.

采集工作完成后通过单片机串口发送至PC机，在基于四元数方程的数学平台中，通过对角度变化及加速度传感器输出量的换算，求得装置相对大地的加速度。

In this paper, some results of the self-conjugate matrices over skew-field of quaternions are given.

本文在[l—5]基础上，给出四元数自共轭矩阵若干结果。

A conclusion that the symmetric product of a self-conjugate matrix is still a self-conjugate matrix was obtained.

给出实四元数体上矩阵对称积的定义，得到了自共轭矩阵的对称积仍是自共轭矩阵的结论。

In terms of the fact that Skinned Mesh Animations based on Matrix palette skinning does not work well for non-quasi-articulated objects, this paper presents a new technology for skin deformation, skinning arbitrary deformation,which can set proxy-joints,automatically construct skinning approximations for arbitrary precomputed animations,and use dual quaternion for skinning .

针对利用MPS驱动的骨骼蒙皮动画对于非关节的对象精度不高的问题，提出了基于MPS的任意变蒙皮，该技术在任意动画上设置代理关节，自动为预先处理的任意动画的每一帧构建蒙皮相似量，利用二重四元数蒙皮，实验表明，SAD不仅能够有效地驱动非关节元素对象提高精度，而且能够充分利用MPS的优点

A method for approximate NURBS skinning ;2. In terms of the fact that Skinned Mesh Animations based on Matrix palette skinning does not work well for non-quasi-articulated objects, this paper presents a new technology for skin deformation, skinning arbitrary deformation,which can set proxy-joints,automatically construct skinning approximations for arbitrary precomputed animations,and use dual quaternion for skinning .

针对利用MPS驱动的骨骼蒙皮动画对于非关节的对象精度不高的问题，提出了基于MPS的任意变蒙皮，该技术在任意动画上设置代理关节，自动为预先处理的任意动画的每一帧构建蒙皮相似量，利用二重四元数蒙皮，实验表明，SAD不仅能够有效地驱动非关节元素对象提高精度，而且能够充分利用MPS的优点。

Except for one thing: you don\'t have a good reason to use quaternions yet.

但除了一件事情，你还没有明白为何要使用四元数的原因。

The concept of Quaternions should be clearly understood.

在四元数的概念应该明确的理解。

Before discussing why you would want to use quaternions, there\'s one more thing that needs to be explained.

在讨论你为什么要使用四元数之前，还有最后一个需要解决的问题。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。