In the nomenclature chapter we denote the fixed inertial frame of reference E as [x.sub.2][y.sub.2][z.sub.2], and the moving noninertial frame of reference B as [x.sub.1][y.sub.1][z.sub.1], which is rigidly bounded with the crane boom [BO.sub.2].
For generalized coordinates we assume the rectangular coordinates [x.sub.1], [y.sub.1], and [z.sub.1] of the load M in the moving noninertial frame of reference B and the angle [[phi].sub.e] of crane boom [BO.sub.2] slewing in the horizontal plane ([x.sub.1][y.sub.1]) with the angular velocity [[omega].sub.e] around the vertical axis [O.sub.2][z.sub.2].
We denote the fixed inertial coordinate system as [x.sub.2][y.sub.2][z.sub.2] and the moving noninertial frame
of reference as [x.sub.1][y.sub.1][z.sub.1], which is rigidly bounded with the crane boom B[O.sub.2].
The Navier-Stokes equations in a noninertial frame of reference are expressed as
Linear acceleration components should be added in case one wants to express the equations of motion in a general noninertial frame.
Therefore, it is possible to implement a conservative formulation in terms of the conservative variables [??] defined in (2) and the introduction of the ALE approach permits a local application of the noninertial frame of reference as a building block in a more complex configuration framework, without any interface between the noninertial and inertial part of the same mesh, because this formulation guarantees the flux conservation.
Extending his special theory to noninertial frames
(those which were accelerating with respect to one another), Einstein, in his general theory of relativity, reconceived of the "force of gravity" as an acceleration resulting from the curvature of space-time rather than as some mysterious force acting at a distance, as it was in Newtonian mechanics.