ABSTRACT
We consider a vector b which is referred to an instantaneous coordinate system with base vectors ex, ey, and ez. Suppose that in a time increment dt there is rotation of the x-y plane clockwise about the z-axis through a small angle dc, generating a new vector b0, and giving rise to the new coordinates x 0, y 0, z 0 in which z 0
coincides with z. This rotation is depicted in Figure 12.1. Note: A negative rotation of the coordinate system is equivalent to a positive rotation of the vector about the instantaneously fixed coordinate system. Prior to the rotation, the vector may be expressed as bT¼ {bx by bz}. For the moment we assume that bx, by, and bz are constants.
