Unformatted text preview: (ad2 + (a2I2 + (w3)2 = 1, or simply (4) aiai = 1. As a further illustration, consider a line element (dx, dy, d z ) in a three- dimensional Euclidean space with rectangular Cartesian coordinates x, y, z. The square of the length of the line element is (5) ds2 = dx2 + dy2 + d z 2 . If we define (6) dx’ = d x , dx2 = dy , dx3 = d z , and Then (5) may be written as (8) ds2 = bijdxidx’, with the understanding that the range of the indices i and j is 1 to 3. Note that there are two summations in the expression above, one over i and one over j. The symbol 6ij as defined in Eq. (7) is called the Kroneclcer delta....
View Full Document
This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.
- Fall '05