[Illustration: FIG. 3.]
14. It is important to distinguish between two types of strain: the
"rotational" type and the "irrotational" type. The distinction is
illustrated in fig. 3, where the figure A"B"C"D" is obtained from the
figure ABCD by contraction parallel to AC and extension parallel to BD,
and the figure A'B'C'D' can be obtained from ABCD by the same
contraction and extension followed by a rotation through the angle
A"OA'. In strains of the irrotational type there are at any point three
filaments at right angles to each other, which are such that the
particles which lie in them before strain continue to lie in them after
strain. A small spherical element of the body with its centre at the
point becomes a small ellipsoid with its axes in the directions of these
three filaments. In the case illustrated in the figure, the lines of the
filaments in question, when the figure ABCD is strained into the figure
A"B"C"D", are OA, OB and a line through O at right angles to their
plane. In strains of the rotational type, on the other hand, the single
existing set of three filaments (issuing from a point) which cut each
other at right angles both before and after strain do not retain their
directions after strain, though one of them may do so in certain cases.
In the figure, the lines of the filaments in question, when the figure
ABCD is strained into A'B'C'D', are OA, OB and a line at right angles to
their plane before strain, and after strain they are OA', OB', and the
same third line. A rotational strain can always be analysed into an
irrotational strain (or "pure" strain) followed by a rotation.