Computer Formulation of the Equations of Motion Using Tensor Notation

A means is described for extending the area
of application of digital computers beyond the 
numerical data processing stage and reducing the need for
human participation in the formulation of certain 
types of computer problems.  By the use of tensor calculus
and a computer language designed to facilitate 
symbolic mathematical computation, a method has been
devised whereby a digital computer can be used to 
do non-numeric work, that is, symbolic algebraic manipulation
and differentiation. To illustrate the 
techniques involved, a digital computer has been used
to derive the equations of motion of a point mass 
in a general orthogonal curvilinear coordinate system.
 Since this operation involves a formulation in 
terms of first- and second-order differential coefficients,
it provides a good demonstration of a computer's 
capability to do non-numeric work and to assist in the
formulation process which normally precedes the 
numerical data processing stage.  Moreover, this particular
problem serves to illustrate the advantages 
of the mathematical techniques employed.  With the program
prepared for this purpose the computer will 
derive the equations of motion in any coordinate system
requested by the user.   Results are presented 
for the following coordinate systems: cylindrical
polar, spherical polar, and prolate spheroidal.

CACM September, 1967

Howard, J. C.

CA670903 JB February 27, 1978  3:58 PM

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