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verscor
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There are 7 letters in VERSCOR ( C3E1O1R1S1V4 )
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In mathematics, a versor is a quaternion of norm one (a unit quaternion). * Each versor has the form* * * * q * = * exp * * ( * a * * r * * ) * = * cos * * a * + * * r * * sin * * a * , * * * * r * * * 2 * * * = * − * 1 * , * * a * ∈ * [ * 0 * , * π * ] * , * * * {\displaystyle q=\exp(a\mathbf {r} )=\cos a+\mathbf {r} \sin a,\quad \mathbf {r} ^{2}=-1,\quad a\in [0,\pi ],} * where the r2 = −1 condition means that r is a unit-length vector quaternion (or that the first component of r is zero, and the last three components of r are a unit vector in 3 dimensions). In case a = π/2, the versor is termed a right versor. * The corresponding 3-dimensional rotation has the angle 2a about the axis r in axis–angle representation. * The word is derived from Latin versare = "to turn" with the suffix -or forming a noun from the verb (i.e. versor = "the turner"). It was introduced by William Rowan Hamilton in the context of his quaternion theory. |