ABSTRACT

We first consider rotation about a fixed axis. The coordinate system is embedded in the fixed point and rotates. The undeformed position vector, X′ in the rotated system is related to its counterpart, X, in the unrotated system by X′=Q(t)X. The counterpart for the deformed position is x′=Q(t)x. The displacement also satisfies u′=Q(t)u. The rotation is represented by the “axial” vector, ω, satisfying . (Recall that

is antisymmetric). The time derivatives in rotating coordinates satisfy

(12.1)

where imply differentiation with the coordinate system instantaneously fixed. The rightmost four terms in (12.1) are called the translational, Coriolis, centrifugal, and angular accelerations, respectively.