Bi-cyclide and flat-ring cyclide coordinate surfaces: correction of two expressions
HTML articles powered by AMS MathViewer
- by Philip W. Kuchel, Brian T. Bulliman and Edward D. Fackerell PDF
- Math. Comp. 49 (1987), 607-613 Request permission
Abstract:
Bi-cyclide and flat-ring cyclide coordinates are three-dimensional rotational coordinate systems based on conformal transformations using the Jacobian elliptic function sn. We have checked the previously published formulae of these systems (P. Moon and D. E. Spencer. Field Theory Handbook, Springer-Verlag, Berlin, 1971). In both cases the expression for the rotation-cyclide surfaces was incorrect: thus we present rederivations. The expressions were verified with the symbolic-algebraic computation package MACSYMA.References
- F. Bowman, Introduction to elliptic functions with applications, Dover Publications, Inc., New York, 1961. MR 0132214
- Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and scientists, Die Grundlehren der mathematischen Wissenschaften, Band 67, Springer-Verlag, New York-Heidelberg, 1971. Second edition, revised. MR 0277773 Z. H. Endre, P. W. Kuchel & B. E. Chapman, "Cell volume dependence of $^1H$ spin-echo NMR signals in human erythrocyte suspensions: The influence of in situ field gradients," Biochim. Biophys. Acta, v. 803, 1984, pp. 137-144. Mathlab Group, Laboratory for Computer Science, MACSYMA Reference Manual, Version 10, Massachusetts Institute of Technology, Cambridge, Mass., 1983. L. M. Milne-Thomson, Jacobian Elliptic Function Tables: A Guide to Practical Computation with Elliptic Functions and Integrals together with Tables of ${\text {sn}}\mu$, ${\text {cn}}\mu$, ${\text {dn}}\mu$, $Z(u)$, Macmillan, London, 1970.
- Parry Moon and Domina Eberle Spencer, Cylindrical and rotational coordinate systems, J. Franklin Inst. 252 (1951), 327–344. MR 43157, DOI 10.1016/0016-0032(51)91054-X
- Parry Moon and Domina Eberle Spencer, Some coordinate systems associated with elliptic functions, J. Franklin Inst. 255 (1953), 531–543. MR 57392, DOI 10.1016/0016-0032(53)90302-0
- Parry Moon and Domina Eberle Spencer, Field theory for engineers, Van Nostrand Series in Electronics and Communications, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1961. MR 0121018
- P. Moon and D. E. Spencer, Field theory handbook, 2nd ed., Springer-Verlag, Berlin, 1988. Including coordinate systems, differential equations and their solutions. MR 947546
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Math. Comp. 49 (1987), 607-613
- MSC: Primary 33A25
- DOI: https://doi.org/10.1090/S0025-5718-1987-0906193-3
- MathSciNet review: 906193