TABLE OF CONTENTS The solution of physical problems can often be simplified if it is expressed in a particular curvilinear coordinate system instead of the classical cartesian coordinate system.
The mathematical presentation of this subject follows the evolution of ideas as presented in (Malvern, 1969; Soos and Teodosiu, 1983). Our development of programming is built upon the kernel of an existing standard MATHEMATICA package, vectorAnalysis. Our additions and modifications are grouped together in the form of a new package called Tensor2Analaysis.
Let us introduce a new system of coordinates ? 1 , ? 2 , ? 3 related to the cartesian coordinates by the functions
We shall assume that the functions can be inverted and possess sufficient smoothness properties. The inverse transformations will be denoted by
The above smoothness and inversibility hypothesis implies that the Jacobian matrix has a nonvanishing determinant in the domain considered:
A point P in the Euclidean space can be identified by its position vector, denoted by
where i k , k=1, 2, 3 denote the basis vectors of the cartesian system. The point P can be identified either by the cartesian coordinates ( x 1 , x 2 , x 3) or by the curvilinear coordinates ( ? 1 , ? 2 , ? 3).
The operators JacobianMatrix and JacobianDeterminant are already...
