Rodrigues' rotation formula gives an efficient method for computing the rotation matrix
corresponding to a rotation by an angle about a fixed axis specified by the unit vector . Then is given by
where
is the identity matrix
and
denotes the antisymmetric matrix with entries
(4)
Note that the entries in this matrix are defined analogously to the differential
matrix representation of the curl operator.
Note that
(5)
so applying the rotation matrix given by Rodrigues' formula to any point on the rotation axis returns the same point.
See also Rotation Formula ,
Rotation
Matrix
This entry contributed by Serge
Belongie
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References Brockett, R. W. "Robotic Manipulators and the Product of Exponentials Formula." In Mathematical
Theory of Networks and Systems. Proceedings of the International Symposium Held at
the Ben Gurion University of the Negev, Beer Sheva, June 20-24, 1983 (Ed.
P. A. Fuhrmann). Berlin: Springer-Verlag, pp. 120-127, 1984. Murray,
R. M.; Li, Z.; and Sastry, S. S. A
Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press,
1994. Referenced on Wolfram|Alpha Rodrigues' Rotation Formula
Cite this as:
Belongie, Serge . "Rodrigues' Rotation Formula." From MathWorld --A Wolfram Web Resource, created by Eric
W. Weisstein . https://mathworld.wolfram.com/RodriguesRotationFormula.html
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