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A new
quaternion: Unit vector division quaternion
Fuad Okay
Department of Civil Engineering, Kocaeli University, Kocaeli,
Turkey.
E-mail:
fuadokay@yahoo.com.
Tel: +90 262 303 3274, +90 533 445 6992(GSM).
Accepted 16 July, 2010 |
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It is well known that, quaternion algebra allows the
defining division of 3-D vectors. Division of vectors has
many applications in applied mathematics and mechanics.
However, indicial notation is widely used in the branches
mentioned above. It is shown in this paper that division of
orthonormal vectors can be conveniently handled by a simple
operator. This operator can be used in the division of two
arbitrary vectors and allows the expression of vector
division using indicial notation. This new operator, which
is a quaternion itself, can be also used in expressing
quaternion product of two vectors, and the derivative of a
vector with respect to a vector.
Key words:
Quaternion, vector quaternions, Einstein’s summation
convention.
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