However, there are two major problems for constraining finite rotation:

2.

A finite rotation through angle ? about this axis may be seen as a succession of small rotations about the same axis.

3.

With these rules, these matrices do not satisfy all the same properties as ordinary finite rotation matrices under the usual treatment of infinitesimals.

4.

In recent times it is easier to determine finite rotations as transforms and ridges are respectively perpendicular and parallel to the direction of a finite rotation pole.

5.

In recent times it is easier to determine finite rotations as transforms and ridges are respectively perpendicular and parallel to the direction of a finite rotation pole.

6.

But one must always be careful to distinguish ( the first order treatment of ) these infinitesimal rotation matrices from both finite rotation matrices and from Lie algebra elements.

7.

When applied to continents, it is possible to define finite rotation with paleomagnetic poles; that is, describe the certain motion of a continent based on records of its paleomagnetic poles.

8.

When contrasting the behavior of finite rotation matrices in the BCH formula above with that of infinitesimal rotation matrices, where all the commutator terms will be second order infinitesimals one finds a bona fide vector space.

9.

Combining two successive rotations, each represented by an Euler axis and angle, is not straightforward, and in fact does not satisfy the law of vector addition, which shows that finite rotations are not really vectors at all.

10.

Again, a finite rotation can be made from lots of small rotations, replacing ? " ? " by and taking the limit as " N " tends to infinity gives the rotation operator for a finite rotation.

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