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Unformatted text preview: r a geological “stage”.
Instantaneous rotations: Describe rotations for
an infinitely small period of time, i.e. present day
plate motions (angular velocity vectors).
Finite rotations: Describe rotations for a finite
time interval in the geological past; (total) finite
rotations reconstruct a plate from its present day
position to a past position. OCE 661 Equivalent rotation
• No matter what set of rotations are applied to a
rigid body one single equivalent rotation can
restore the body to its original position.
–> True both on a plane and on a sphere.
• After applying a complex set of rotations to a pair
of plates, a single rotation can be found that will
restore the original position of the plates. Finite rotations not stationary with time
• Consider three plates, and three rotation poles that
describe their relative motion to each other, i.e.
AWB, BWC, and CWA.
• If AWB and BWC are fixed in space and time, then
CWA will change continuously through time.
–> As there is no reason to assume that any set of
finite rotation poles are stationary, then all must be
• However, it is found in the real world that some
rotation poles seem to vary very little in position
even over long periods of time. OCE 661 FINITE ROTATIONS: THEORY OF FINITE ROTATIONS
Non-commutativity of finite plate rotations
• Finite rotations are non-commutative.
• Rotations are mathematically described by matrix
transformations and are sensitive to the order in which the
transformations are carried out.
• Unlike in the case of vectors, if A, B are matrices,
then AB ¹ BA. This can be shown easily by rotating a book: OCE 661 Summary
(1) All transform faults are small circles about the pole of
rotation representing the motion between the two
(2) The velocity of separation of two plates increases as
the sine of the colatitude away from the rotation pole.
(3) At a triple junction the velocity vectors sum to zero.
(4) Taking any path over the surface of the earth
beginning and ending on...
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This document was uploaded on 01/26/2014.
- Winter '14