 To obtain the equations, it is convenient to imagine a rigid body attached to the frames and consider a coordinate system that is fixed with respect to the rigid body.Then we will study the coordinate transformations between this coordinate and the fixed "laboratory" system.As shown in the figure on the right, the lab system's origin is at point "O", the rigid body system origin is at and the vector from "O" to is R. A particle ("i") in the rigid body is located at point P and the vector position of this particle is R"i" in the lab frame, and at position r"i" in the body frame.