Coordinate transformation matrix

Reference: "Robotics, Vision and Control", "torpedo sailing Mechanics", other dissertations

To see the open question papers and found coordinate transformation matrix actually stuck a fundamental part of this, some of the online discussion or else the lack of intermediate process, or even wrong, then order a bit.
ps I did not expect "Robotics, Vision and Control" has been that this little book and study the relationship became the last straw.




Right-hand rule
About a rotation vector

The book is given directly around each x, y, z rotation matrix sita-axis angle, and this is often seen three matrices. But it is worth noting that these three matrices actually coordinate system transformation matrix formula is

原坐标=[坐标转换矩阵]新坐标

And we usually expect novelty coordinates, so

新坐标=[坐标转换矩阵的逆]原坐标

Also, because of the orthogonal matrix, i.e., inverse transpose

新坐标=[坐标转换矩阵的转置]原坐标

Read some papers, although the final total of the coordinate transformation matrix is ​​right, but the process was concluded that the lack of a coordinate transformation matrix transpose operation, which is incorrect (although the process will generally be skipped readers), as follows:

In addition, and some books ( "torpedo sailing mechanics") and papers in front of the derivation is omitted, the coordinate transformation matrix is ​​given directly point to point, people feel very strange, even skeptical conclusion is correct. (But later found that this derivation is the transposed matrix)

Meanwhile, depending on the establishment of the coordinate system, there are differences in the rotation order, but there are certain criteria.

Rotation order on the following book "torpedo sailing mechanics" because the establishment of "East - Day - South" ground coordinate system, that means that the x-axis east, y-axis refers to the day, z-axis guide, the corresponding body coordinate mine Department is also in accordance with the "East - day - South" to use, its rotation order yzx, respectively rotated course - pitch - roll angle .
And the above rotation matrix from certain airline books and papers, as is the z-axis in the vertical direction (z-axis refers to some days, the z-axis refers to some ...), angular rotation of the common navigation order is ZYX, the same in accordance with the heading - pitch - roll angle sequence.

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Origin www.cnblogs.com/j-c-y/p/12010152.html