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