Engineering topics
Publications and source records attributed to Stoutemyer, D. R..
The computer algebra language MACSYMA enables the programmer to include symbolic physical units in computer calculations, and features automatic detection of dimensionally-inhomogeneous formulas and conversion of inconsistent units in a dimensionally homogeneous formula. Some examples illustrate these features.
Attempts to achieve tasteful automatic employment of the identities sin sq x + cos sq x = 1 and cos sq h x -sin sq h x = 1 in a manner which truly minimizes the complexity of the resulting expression are described. The disappointments of trigonometric reduction, trigonometric expansion, pattern matching, Poisson series, and Demoivre's theorem are related. The advantages of using the method of comparative combinatorial substitutions are illustrated.
A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.