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