Hanspeter Schaub, and John L. Junkins, Analytical Mechanics of Space Systems (Second Edition), Reston, VA: American Institute of Aeronautics and Astronautics, 2009.
I just roughly read section 3, mainly about the attitude basics and kinematics.
3. Rigid Body Kinematics
3.2 Direction Cosine Matrix
Use the shorthand vectrix notation
（这里似乎和linear algebra中对basis的表示不同：linear algebra中通常把基底也表示为列向量，但是这里把基底作为了行向量，所以在后续对[C]的定义和运算中，就会存在一个转置T的区别。） （已经搞明白了，见本节后面的中文讨论）
is a generic rigid body;
can be a inertial coordinate system.
where is the angle between and .
The direction cosine matrix is
In a standard coordinate transformation setting, the matrix is typically not restricted to projecting one set of base vectors from one reference frame onto another. Rather, the most powerful feature of the direction cosine is the ability to directly project (or transform) an arbitrary vector, with components written in one reference frame, into a vector with components written in another reference frame.
（vector是固定不动的，只是对components in frame进行变换。这是passive transformation。）
Using Eq. (3.5) or (3.7)
Let us use the following notation to label the various direction cosine matrices.
The matrix maps vectors written in the N frame into vectors written in the frame.
Analogously, the matrix maps vectors in the frame into frame vectors and so on.
where the skew-symmetric tilde matrix is
3.3 Euler Angles
The kinematic differential equation of the (3-2-1) Euler angles
Kinematic equations for other sets of Euler angles can be obtained similarly, see Appendix B of the textbook.
3.4 Principal Rotation Vector
the principal rotation vector is not well suited for use in small motion feedback control type applications where the reference state is the zero rotation.
less attractive to describe large arbitrary rotations as compared to some other, closely related, attitude parameters that will be presented in the next few sections.
3.5 Euler Parameters (Quaternions)
Another popular set of attitude coordinates are the four Euler parameters (quaternions).
If defines DCM that transform vector components in to those in ,
then the converted quaternion describes the attitude of the frame relative to the frame.
Kinematic equations (taking the derivative of , then substituting from Eq.(3.27), and using Eq.(3.94) to turn back to ):
Define , then
3.9 Homogeneous Transformations
Consider both translation and rotation,
Define homogeneous transformation,
and the position vector
then we have
This formula is very convenient when computing the position coordinate of a chain of bodies such as are typically found in robotics applications.