Leibnitz rule three-dimensional

In a customary interpretation the Reynolds transport theorem provides the link between the system and control volume representations, while the Leibnitz s theorem is a three dimensional version of the integral rule for differentiation of an integral. There are several notations used for the transport theorem and there are numerous forms and corollaries. 

A three dimensional extension of the Leibnitz rule for differentiating an integral is relevant for the derivation of the governing transport equations L In the material (Lagrangian) representation of continuum mechanics a representative particle of the continuum occupies a point in the initial configuration of the continuum at time t = 0 and has the position vector = (Ci, 2, Cs)-In this -space the coordinates are called the material coordinates. In the Eulerian representation the particle position vector in r-space is defined by r = (ri,r2,r3). The coordinates ri,r2,r3 which gives the current position of the particle are called the spatial coordinates. Let be any scalar, vector... 

A three dimensional extension of the Leibnitz rule for differentiating an integral is relevant for the derivation of the governing transport equations. ... 

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