1.0 KiB
Vectors
- magnitude 大小
- direction 方向
- sense 正负
Unit vectors 模=1
Reference Frames Euclidean 3D Space:all points in some 3D space
Observer of position + motion
motion is a function of the obsersiver's orientation
Frame of reference "reference frame" is a set of all Euclidean points fixed to the observer. An abstraction to understand motion
We will fix 3 right-handed mutually perpendiculur unit vectors to a reference frame and use them to determine orientation among reference frames
互相垂直，右手坐标系，满足叉乘规律
Simple 2D orientation
B关于A的的变换矩阵 ---- 方向余弦矩阵 direct cosine matrix or 旋转矩阵 rotation matrix of B with respect to A
或者称之为 Right handed rotation of B with respect to A about the shared Z unit vector through the angle theta
Successive Rotations
C^[C]^A = C^[C]^B * B^[C]^A
Euler Angles 3 successive simple rotations about shared axes that allows for arbitrary orientation of two reference frames with two additional or auxiliary reference frames