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Deformed Surface Orientation

Suppose we want to determine how much of the orientation of the surface of a deformed body has changed from its original orientation ...

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A normal to a surface is often used to describe the surface. The angle between two normal vectors can be used to describe the amount of rotation that the original surface has gone through. In this example, we assume N^ to be e3^. Since e3^ is a unit vector in the z-direction, we assume that the original surface is the two dimensional x-y plane. Note that since e3^ is a unit vector, its magnitude is 1. Now suppose the original surface rotates that the normal vector to the new surface is defined as xe1^ + ye2^ + ze3^. We need to make it ...