Kinematics/3D Coordinate Systems

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Fixed Rectangular Coordinate Frame[edit]

In this coordinate system, vectors are expressed as an addition of vectors in the x, y, and z direction from a non-rotating origin. Usually is a unit vector in the x direction, is a unit vector in the y direction, and is a unit vector in the z direction.

The position vector, (or ), the velocity vector, , and the acceleration vector, are expressed using rectangular coordinates in the following way:

Note: ,

Rotating Coordinate Frame[edit]