An Algorithm for Deriving the Equations of
Mathematical Physics by Symbolic Manipulation

A method is described whereby a digital computer
can be used to derive the equations of mathematical 
physics in any curvilinear coordinate system requested
by the user.  The effectiveness of the technique 
is demonstrated by using it to derive the Navier-Stokes
equations of fluid motion and the continuity 
equation.  To derive these equations by this method, the
user need know only the coordinate transformation 
equations relating the curvilinear coordinates of interest
to an orthogonal Cartesian triad. When this 
program is used and the coordinate transformation equations
are supplied as input, the computer will 
derive the Navier-Stokes equations and the continuity
equation.  The equations obtained will be relative 
to the curvilinear coordinate system specified by the
transformation equations used as input.  In this 
paper the emphasis is on theoretical considerations and
methodology rather than on programming details. 
 Results are presented for cylindrical polar
and spherical polar coordinate systems.

CACM December, 1968

Howard, J. C.
Tashjian, H.

FORMAC, Navier-Strokes equations, continuity equation,
tensor, tensor equation, curvilinear coordinate 
systems, FORTRAN, symbolic manipulation

3.21 3.25 3.29 4.12 4.29

CA681202 JB February 21, 1978  2:02 PM

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