The difference between the two displacement vectors, \ vec r _ B-\ vec r _ A, represents the location of B as seen from A.
22.
The distance d between P and Q, or the length of the displacement vector \ overrightarrow { P Q } = ( x, y, z ), is
23.
Likewise, it makes sense to add a displacement vector to a point of an affine space, resulting in a new point translated from the starting point by that vector.
24.
With this in mind we may then define a " position vector " of a point in space as the displacement vector mapping a given origin to that point.
25.
A " displacement field " is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration.
26.
However, instead of calculating up the distances between subsequent points, we need to calculate their displacement vectors, ? "'r " "'i ".
27.
For some purposes it is desirable to identify tangent vectors at a point with " displacement vectors " at, which is, of course, admissible by essentially the same canonical identification.
28.
There are six independent components of the stress tensor which need to be determined, yet in the displacement formulation, there are only three components of the displacement vector which need to be determined.
29.
Moreover, the equation allow us to calculate the natural frequency only if the eigenvector ( as well as any other displacement vector ) \ textbf { u } _ { m } is known.
30.
The constraints on the strain tensor are derivable directly from the definition of the strain tensor as a function of the displacement vector field, which means that these constraints introduce no new concepts or information.
