. The computational cost of renormalizing a quaternion, however, is much less than for normalizing a 3 3 matrix. . {\displaystyle -R{\dot {\theta }}^{2}\mathbf {e} _{r}} From the origin, in any direction, is the same rotation axis, with the scale of the angle equivalent to the distance from the origin. T and Stars, planets and similar bodies all spin around on their axes. Further details about the mathematical methods to represent the orientation of rigid bodies and planes in three dimensions are given in the following sections. {\displaystyle 0
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